Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Linear preservers of two-sided right matrix majorization on $mathbb{R}_{n}$4514585365410.15352/aot.1709-1225ENAhmad MohammadhasaniAsma Ilkhanizadeh ManeshRafsanjan University of Vali AsrJournal Article20170906A nonnegative real matrix $Rin textbf{M}_{n,m}$ with the property that all its row sums are one is said to be row stochastic. For $x, y in mathbb{R}_{n}$, we say $x$ is right matrix majorized by $y$ (denoted by $xprec_{r} y$) if there exists an $n$-by-$n$ row stochastic matrix $R$ such that $x=yR$. The relation $sim_{r}$ on $mathbb{R}_{n}$ is defined as follows. $xsim_{r}y$ if and only if $ xprec_{r} yprec_{r} x$. In the present paper, we characterize the linear preservers of $sim_{r}$ on $mathbb{R}_{n}$, and answer the question raised by F. Khalooei [Wavelet Linear Algebra textbf{1} (2014), no. 1, 43--50].http://www.aot-math.org/article_53654_59d049b74ce0e9accb168ebb4db2105b.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces4594725408710.15352/aot.1708-1220ENMohammad AlomariJournal Article20170821In this work, generalization of some inequalities for continuous h-synchronous (h-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved. .http://www.aot-math.org/article_54087_0a5c931295412bb7ca2a95f8feda0573.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Perturbation of minimum attaining operators4734905427010.15352/aot.1708-1215ENJadav GaneshDepartment of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Medak(Dist),
Telangana 502285, IndiaGolla RameshIIT HyderabadDaniel SukumarDepartment of Mathematics, IIT Hyderabad, Kandi, Sangareddy, Medak(Dist),
Telangana 502285, IndiaJournal Article20170810We prove that the minimum attaining property of a bounded linear operator on a Hilbert space $H$ whose minimum modulus lies in the discrete spectrum, is stable under small compact perturbations. We also observe that given a bounded operator with strictly positive essential minimum modulus, the set of compact perturbations which fail to produce a minimum attaining operator is smaller than a nowhere dense set. In fact it is a porous set in the ideal of all compact operators on $H$. Further, we try to extend these stability results to perturbations by all bounded linear operators with small norm and obtain subsequent results.http://www.aot-math.org/article_54270_bc17d5d42fb655dade72954a6c56fd0a.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Besicovitch almost automorphic solutions of nonautonomous differential equations of first order4915065449210.15352/aot.1711-1257ENMarko KosticJournal Article20171105The main purpose of this paper is to analyze the existence and uniqueness of Besicovitch almost automorphic solutions and weighted Besicovitch pseudo-almost automorphic solutions of nonautonomous differential equations of first order. We provide an interesting application of our abstract theoretical results.http://www.aot-math.org/article_54492_65ee01700cc48f0cf7bef87718a3f617.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701A Kakutani-Mackey-like theorem5075215602910.15352/aot.1712-1270ENMarina HaralampidouDepartment of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, GreeceKonstantinos TzironisDepartment of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, GreeceJournal Article20171205We give a partial extension of a Kakutani-Mackey theorem for quasi-complemented vector spaces. This can be applied in the representation theory of certain complemented (non-normed) topological algebras. The existence of continuous linear maps, in the context of quasi-complemented vector spaces, is a very important issue in their study. Relative to this, we prove that every Hausdorff quasi-complemented locally convex space has continuous linear maps, under which a certain quasi-complemented locally convex space, turns to be pre-Hilbert.http://www.aot-math.org/article_56029_e54f74797c92d1f650c19dab2b77f90e.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701$T1$ theorem for inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces and its application5225375707210.15352/aot.1709-1236ENFanghui LiaoZongguang LiuChina University of Mining and Technology(Beijing)Hongbin WangJournal Article20170922Using Calder'{o}n's reproducing formulas and almost orthogonal estimates, the $T1$ theorem for the inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces is obtained. As an application, new characterizations for these spaces with ``half" the usual conditions of the approximate to the identity are presented.http://www.aot-math.org/article_57072_888f8c2b8da0ea7fac2ff9eeb211dc2a.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Fixed points of a class of unitary operators5385505740310.15352/aot.1710-1244ENNamita DasP. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, IndiaJitendra BeheraP. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, IndiaJournal Article20171013In this paper, we consider a class of unitary operators defined on the Bergman space of the right half plane and characterize the fixed points of these unitary operators. We also discuss certain intertwining properties of these operators. Applications of these results are also obtained.http://www.aot-math.org/article_57403_9ef2e37b57c571444740ffc979926104.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Well-posedness issues for a class of coupled nonlinear Schr"odinger equations with critical exponential growth5515815744410.15352/aot.1709-1227ENHanen HezziUniversity of Tunis El Manar, Faculty of Sciences of Tunis, LR03ES04 partial differential equations and applications, 2092 Tunis, TunisiaJournal Article20170907The initial value problem for some coupled nonlinear Schrodinger equations in two space dimensions with exponential growth is investigated. In the defocusing case, global well-posedness and scattering are obtained. In the focusing sign, global and non global existence of solutions are discussed via potential well- method.http://www.aot-math.org/article_57444_2c0e0da5d64c8fabde55e8ee06badb79.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Closedness and invertibility for the sum of two closed operators5826055748110.15352/aot.1801-1297ENNikolaos RoidosInstitute of Analysis, Leibniz University of Hanover, GermanyJournal Article20180119We show a Kalton--Weis type theorem for the general case of non-commuting operators. More precisely, we consider sums of two possibly non-commuting linear operators defined in a Banach space such that one of the operators admits a bounded $H^infty$-calculus, the resolvent of the other one satisfies some weaker boundedness condition and the commutator of their resolvents has certain decay behavior with respect to the spectral parameters. Under this consideration, we show that the sum is closed and that after a sufficiently large positive shift it becomes invertible, and moreover sectorial. As an application we recover a classical result on the existence, uniqueness and maximal $L^{p}$-regularity for solutions of the abstract linear non-autonomous parabolic problem.http://www.aot-math.org/article_57481_9dc50d9f66c3c3266ee8dd0c78d135ef.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Parallel iterative methods for solving the common null point problem in Banach spaces6066195773510.15352/aot.1710-1246ENTuyen TruongDepartment of Mathematics and Informatics, Thainguyen University of Sciences, Thai Nguyen, VietnamNguyen TrangFaculty of International training, Thainguyen University of Technology, Thai Nguyen, VietnamJournal Article20171016We consider the common null point problem in Banach spaces. Then, using the hybrid projection method and the $varepsilon $- enlargement of maximal monotone operators, we prove two strong convergence theorems for finding a solution of this problem.http://www.aot-math.org/article_57735_78e447c015a1cc99204e72dafc32433e.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Complex isosymmetric operators6206315775910.15352/aot.1712-1267ENMuneo ChōKanagawa UniversityJi Eun LeeDepartment of Mathematics and Statistics, Sejong University, Seoul 143-747, KoreaT. PrasadDepartment of Mathematics, Cochin university of Science and Technology, Kochi, IndiaKôtarô TanahashiDepartment of Mathematics, Tohoku Medical and Pharmaceutical University, Sendai 981-8558, JapanJournal Article20171203In this paper, we introduce complex isosymmetric and $(m,n,C)$-isosymmetric operators on a Hilbert space $mathcal H$ and study properties of such operators. In particular, we prove that if $T in {mathcal B}(mathcal H)$ is an $(m,n,C)$-isosymmetric operator and $N$ is a $k$-nilpotent operator such that $T$ and $N$ are $C$-doubly commuting, then $T + N$ is an $(m+2k-2, n+2k-1,C)$-isosymmetric operator. Moreover, we show that if $T$ is $(m,n,C)$-isosymmetric and if $S$ is $(m',D)$-isometric and $n'$-complex symmetric with a conjugation $D$, then $T otimes S$ is $(m+m'-1,n+n'-1,C otimes D)$-isosymmetric.http://www.aot-math.org/article_57759_b9d4decc8062d9cb38ddba2ce3edb0bc.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Variant versions of the Lewent type determinantal inequality6326385802710.15352/aot.1711-1259ENAli MorassaeiJournal Article20171109In this paper, we present a refinement of the Lewent determinantal inequality and then, we show that the following inequality holds begin{align*} &detfrac{I_{mathcal{H}}+A_1}{I_{mathcal{H}}-A_1}+detfrac{I_{mathcal{H}}+A_n}{I_{mathcal{H}}-A_n}-sum_{j=1}^nlambda_j detleft(frac{I_{mathcal{H}}+A_j}{I_{mathcal{H}}-A_j}right)\ & ge detleft[left(frac{I_{mathcal{H}}+A_1}{I_{mathcal{H}}-A_1}right)left(frac{I_{mathcal{H}}+A_n}{I_{mathcal{H}}-A_n}right)prod_{j=1}^n left(frac{I_{mathcal{H}}+A_j}{I_{mathcal{H}}-A_j}right)^{-lambda_j}right],, end{align*} where $A_jinmathbb{B}(mathcal{H})$, $0le A_j < I_mathcal{H}$, $A_j's$ are trace class operators and $A_1 le A_j le A_n~(j=1,cdots,n)$ and $sum_{j=1}^nlambda_j=1,~ lambda_j ge 0~ (j=1,cdots,n)$. In addition, we present some new versions of the Lewent type determinantal inequality.http://www.aot-math.org/article_58027_e4993959d2838f85d7a990cb957c644c.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701wUR modulus and normal structure in Banach spaces6396465806810.15352/aot.1801-1295ENJi GaoJournal Article20180114Let $X$ be a Banach space. In this paper, we study the properties of wUR modulus of $X$, $delta_X(varepsilon, f),$ where $0 le varepsilon le 2$ and $f in S(X^*),$ and the relationship between the values of wUR modulus and reflexivity, uniform non-squareness and normal structure respectively. Among other results, we proved that if $ delta_X(1, f)> 0$ for any $fin S(X^*),$ then $X$ has weak normal structure.http://www.aot-math.org/article_58068_bab5247b1aec6e648c85b7d2223d9400.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701The matrix power means and interpolations6476545811110.15352/aot.1801-1288ENDINH Trung HoaRaluca DumitruJose A. FrancoJournal Article20180105It is well-known that the Heron mean is a linear interpolation between the arithmetic and the geometric means while the matrix power mean $P_t(A,B):= A^{1/2}left(frac{I+(A^{-1/2}BA^{-1/2})^t}{2}right)^{1/t}A^{1/2}$ interpolates between the harmonic, the geometric, and the arithmetic means. In this article, we establish several comparisons between the matrix power mean, the Heron mean and the Heinz mean. Therefore, we have a deeper understanding about the distribution of these matrix means.http://www.aot-math.org/article_58111_2db06770ff58292e14a48df88a3e8429.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701$C^*$-algebra distance filters6556815825810.15352/aot.1710-1241ENTristan BiceAlessandro VignatiJournal Article20171010We use non-symmetric distances to give a self-contained account of $C^*$-algebra filters and their corresponding compact projections, simultaneously simplifying and extending their general theory. http://www.aot-math.org/article_58258_60253d2648889c6465fbb303065fad63.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701On Neugebauer's covering theorem6826895825910.15352/aot.1711-1262ENJésus M. AldazJournal Article20171119We present a new proof of a covering theorem of C. J. Neugebauer, stated in a slightly more general form than the original version; we also give an application to restricted weak type (1,1) inequalities for the uncentered maximal operator.http://www.aot-math.org/article_58259_27f6aa7b3ddc36299f175589a7784c20.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701The existence of hyper-invariant subspaces for weighted shift operators6906985811310.15352/aot.1802-1316ENHossein SadeghiUniversity of ZanjanFarzollah MirzapourUniversity of ZanjanJournal Article20180116We introduce some classes of Banach spaces for which the hyperinvariant subspace problem for the shift operator has positive answer. Moreover, we provide sufficient conditions on weights which ensure that certain subspaces of $ell^2_{{beta}}(mathbb{Z})$ are closed under convolution. Finally we consider some cases of weighted spaces for which the problem remains open.http://www.aot-math.org/article_58113_86409cebe989bb55a3992eaaa911aa5a.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Orthogonality of bounded linear operators on complex Banach spaces6997095848210.15352/aot.1712-1268ENKallol PaulDepartment of Mathematics
Jadavpur University
Kolkata 700032
IndiaDebmalya SainIndian Institute of Science, BengaluruArpita MalDepartment of Mathematics
Jadavpur University
Kolkata 700032
IndiaKalidas MandalDepartment of Mathematics
Jadavpur University
Kolkata 700032
IndiaJournal Article20171201We study Birkhoff-James orthogonality of compact linear operators on complex reflexive Banach spaces and obtain its characterization. By means of introducing new definitions, we illustrate that it is possible in the complex case, to develop a study of orthogonality of compact linear operators, analogous to the real case. Furthermore, earlier operator theoretic characterizations of Birkhoff-James orthogonality in the real case, can be obtained as simple corollaries to our present study. In fact, we obtain more than one equivalent characterizations of Birkhoff-James orthogonality of compact linear operators in the complex case, in order to distinguish the complex case from the real case.http://www.aot-math.org/article_58482_7dbaeeafc2780dac3d0996c2d9a48612.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Affine actions and the Yang-Baxter equation7107306010410.15352/aot.1801-1298ENDilian YangJournal Article20180119In this paper, the relations between the Yang-Baxter equation and affine actions are explored in detail. In particular, we classify the injective set-theoretic solutions of the Yang-Baxter equation in two ways: (i) by their associated affine actions of their structure groups on their derived structure groups, and (ii) by the $C^*$-dynamical systems obtained from their associated affine actions. On the way to our main results, several other useful results are also obtained.http://www.aot-math.org/article_60104_5b1e93d062f80db45bd3e9f530226155.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701Characterizing projections among positive operators in the unit sphere7317446034110.15352/aot.1804-1343ENAntonio PeraltaUniversidad de Granada0000-0003-2528-8357Journal Article20180401Let $E$ and $P$ be subsets of a Banach space $X$, and let us define the unit sphere around $E$ in $P$ as the set $$Sph(E;P) :=left{ xin P : |x-b|=1 hbox{ for all } bin E right}.$$ Given a $C^*$-algebra $A$ and a subset $Esubset A,$ we shall write $Sph^+ (E)$ or $Sph_A^+ (E)$ for the set $Sph(E;S(A^+)),$ where $S(A^+)$ denotes the unit sphere of $A^+$. We prove that, for every complex Hilbert space $H$, the following statements are equivalent for every positive element $a$ in the unit sphere of $B(H)$: (a) $a$ is a projection (b) $Sph^+_{B(H)} left( Sph^+_{B(H)}({a}) right) ={a}$. We also prove that the equivalence remains true when $B(H)$ is replaced with an atomic von Neumann algebra or with $K(H_2)$, where $H_2$ is an infinite-dimensional and separable complex Hilbert space. In the setting of compact operators we establish a stronger conclusion by showing that the identity $$Sph^+_{K(H_2)} left( Sph^+_{K(H_2)}(a) right) =left{ bin S(K(H_2)^+) : !! begin{array}{c}s_{_{K(H_2)}} (a) leq s_{_{K(H_2)}} (b), hbox{ and }\ textbf{1}-r_{_{B(H_2)}}(a)leq textbf{1}-r_{_{B(H_2)}}(b) end{array}right},$$ holds for every $a$ in the unit sphere of $K(H_2)^+$, where $r_{_{B(H_2)}}(a)$ and $s_{_{K(H_2)}} (a)$ stand for the range and support projections of $a$ in $B(H_2)$ and $K(H_2)$, respectively.http://www.aot-math.org/article_60341_1b13a753583eb613f2eecd19bf0bb7e9.pdf