Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
On the weak compactness of Weak* Dunford-Pettis operators on Banach lattices
192
200
EN
El Fahri
Kamal
Ibno Tofail University
kamalelfahri@gmail.com
H'michane
Jawad
Moulay Ismail University
hm1982jad@gmail.com
El Kaddouri
Abdelmonim
Ibno Tofail University
elkaddouri.abdelmonaim@gmail.com
Aboutafail
Moulay Othmane
Universite Ibn Tofail
aboutafail@yahoo.fr
10.22034/aot.1612-1078
We characterize Banach lattices on which each positive weak* Dunford--Pettis operator is weakly (resp., M-weakly, resp., order weakly) compact. More precisely, we prove that if $F$ is a Banach lattice with order continuous norm, then each positive weak* Dunford--Pettis operator $T : Elongrightarrow F$ is weakly compact if, and only if, the norm of $E^{prime}$ is order continuous or $F$ is reflexive. On the other hand, when the Banach lattice $F$ is Dedekind $sigma$-complete, we show that every positive weak* Dunford--Pettis operator $T: Elongrightarrow F$ is M-weakly compact if, and only if, the norms of $E^{prime}$ and $F$ are order continuous or $E$ is finite-dimensional.
Weak* Dunford-Pettis operator,weakly compact operator,M-weakly compact operator,order weakly compact operator,DP* property
http://www.aot-math.org/article_44450.html
http://www.aot-math.org/article_44450_933357c2224044441dc197fc6092a9d7.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Two-weight norm inequalities for the higher-order commutators of fractional integral operators
201
214
EN
Caiyin
Niu
niucaiyin@yahoo.com
Xiaojin
Zhang
zxj800225@126.com
10.22034/aot.1612-1075
In this paper, we obtain several sufficient conditions such that the higher-order commutators $I_{alpha,b}^m$ generated by $I_alpha$ and $bin textrm{BMO}(mathbb{R}^n)$ is bounded from $L^p(v)$ to $L^q(u)$, where $frac{1}{q}=frac{1}{p}-frac{alpha}{n}$ and $0
Fractional integrals,BMO,higher-order commutators,two-weight
http://www.aot-math.org/article_44490.html
http://www.aot-math.org/article_44490_12d0701fe5fcfd677d8a14ebcc6ae07d.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Properties of $J$-fusion frames in Krein spaces
215
227
EN
Shibashis
Karmakar
Jadavpur University
shibashiskarmakar@gmail.com
Sk. Monowar
Hossein
Department of Mathematics, Aliah University, IIA/27 New Town, Kolkata - 156, W.B., India
sami_milu@yahoo.co.uk
Kallol
Paul
Jadavpur University
kalloldada@gmail.com
10.22034/aot.1612-1070
In this article we introduce the notion of $J$-Parseval fusion frames in a Krein space $mathbb{K}$ and characterize 1-uniform $J$-Parseval fusion frames with $zeta=sqrt{2}$. We provide some results regarding construction of new $J$-tight fusion frame from given $J$-tight fusion frames. We also characterize an uniformly $J$-definite subspace of a Krein space $mathbb{K}$ in terms of $J$-fusion frame. Finally we generalize the fundamental identity of Hilbert space frames in the setting of Krein spaces.
Krein Space,fusion frames,J- fusion frame,Gramian operator,regular subspace
http://www.aot-math.org/article_44491.html
http://www.aot-math.org/article_44491_64927e80a0e1a76256354362aa602392.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
On the behavior at infinity of certain integral operator with positive kernel
228
236
EN
Homaion
Roohian
University of Applied Science and Technology
homaionroohian@gmail.com
Soroosh
Mohammadi Farsani
s_mbahman@yahoo.com
10.22034/aot.1701-1101
Let $alpha>0$ and $gamma>0$. We consider integral operator of the form$${mathcal{G}}_{phi_gamma}f(x):=frac{1}{Psi_gamma (x)}int_0^x (1-frac{y}{x})^{alpha-1}phi_gamma(y) f(y)dy,,,,, x>0.$$This paper is devoted to the study of the infinity behavior of ${mathcal{G}}_{phi_gamma}$. We also provide separately result on the similar problem in the weighted Lebesgue space.
Integral operators,weighted Lebesgue space,behavior at infinity,convergence almost everywhere
http://www.aot-math.org/article_44569.html
http://www.aot-math.org/article_44569_2d85b42ba7132b3a7409bbf38c7fbe32.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
237
256
EN
Michael
Th.
Rassias
michail.rassias@math.uzh.ch
Bicheng
Yang
bcyang@gdei.edu.cn
10.22034/aot.1703-1132
By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardy-type integral inequalities with the homogeneous kernel are deduced. We also consider the operator expressions.
Hardy-type integral inequality,weight function,equivalent form,Riemann zeta function,operator
http://www.aot-math.org/article_44577.html
http://www.aot-math.org/article_44577_1bdf44135db255e6e380484e7e83915f.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Existence theorems for attractive points of semigroups of Bregman generalized nonspreading mappings in Banach spaces
257
268
EN
Bashir
Ali
bashiralik@yahoo.com
Murtala
Haruna
Harbau
murtalaharbau@yahoo.com
Lawan
Haruna
Yusuf
yulah121@gmail.com
10.22034/aot.1611-1062
In this paper, we establish new attractive point theorems for semigroups of generalized Bregman nonspreading mappings in reflexive Banach spaces. Our theorems improve and extend many results announced recently in the literature.
Bregmann attractive point,Bregman distance,generalized Bregman nonspreading mapping,Legendre function,invariant mean
http://www.aot-math.org/article_44913.html
http://www.aot-math.org/article_44913_f635b05f711ebb978d7b8c937d5de88e.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Boundedness of multilinear integral operators and their commutators on generalized Morrey spaces
269
286
EN
Panwang
Wang
panwangw@gmail.com
Zongguang
Liu
liuzg@cumtb.edu.cn
10.22034/aot.1611-1051
In this paper, we obtain some boundedness of multilinear Calder'on-Zygmund Operators, multilinear fractional integral operators and their commutators on generalized Morrey Spaces.
Calder'on-Zygmund operators,commutators,fractional integral operators,weighted Morrey spaces
http://www.aot-math.org/article_45124.html
http://www.aot-math.org/article_45124_21a043304549ed266e88cf261bd9dd56.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Semigroup homomorphisms on matrix algebras
287
292
EN
Bernhard
Burgstaller
bernhardburgstaller@yahoo.de
10.22034/aot.1702-1121
We explore the connection between ring homomorphisms and semigroup homomorphisms on matrix algebras over rings or $C^*$-algebras. Further, we give a connection between group homomorphisms on the general linear groups of a matrix stable $C^*$-algebra and their potentially extended homomorphisms on the whole $C^*$-algebra.
semigroup,ring,matrix,multiplicative,additive,unique addition,$C^*$-algebra
http://www.aot-math.org/article_45172.html
http://www.aot-math.org/article_45172_88cbac9c3a90003dba4dce5458586234.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Applications of ternary rings to $C^*$-algebras
293
317
EN
Damian
Ferraro
Universidad de la Republica
dferraro@unorte.edu.uy
Fernando
Abadie
Universidad de la Republica
fabadie@cmat.edu.uy
10.22034/aot.1612-1085
We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its corresponding $*$-algebra. We apply this functor to obtain Morita-Rieffel equivalence results between cross-sectional $C^*$-algebras of Fell bundles, and to extend the theory of tensor products of $C^*$-algebras to the larger category of full Hilbert $C^*$-modules. We prove that, like in the case of $C^*$-algebras, there exist maximal and minimal tensor products. As applications we give simple proofs of the invariance of nuclearity and exactness under Morita-Rieffel equivalence of $C^*$-algebras.
ternary rings,Morita-Rieffel equivalence,nuclear,exact
http://www.aot-math.org/article_45350.html
http://www.aot-math.org/article_45350_b879e3ece9015535fc2a911cb1f08e32.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
$k$th-order slant Toeplitz operators on the Fock space
318
333
EN
Shivam Kumar
Kumar
Singh
Ph. D. Scholar, Department of Mathematics, University of Delhi, Delhi, India
shivamkumarsingh14@gmail.com
Anuradha
Gupta
Associate Professor, Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi-110023, India
dishna2@yahoo.in
10.22034/aot.1703-1133
The notion of slant Toeplitz operators $B_phi$ and $k$th-order slant Toeplitz operators $B_phi^k$ on the Fock space is introduced and some of its properties are investigated. The Berezin transform of slant Toeplitz operator $B_phi$ is also obtained. In addition, the commutativity of $k$th-order slant Toeplitz operators with co-analytic and harmonic symbols is discussed.
$k$th-order slant Toeplitz operator,Fock space,Berezin transform
http://www.aot-math.org/article_46068.html
http://www.aot-math.org/article_46068_02a23743ff810705868374e0b4283c1b.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Comparison results for proper multisplittings of rectangular matrices
334
352
EN
Chinmay
Kumar
Giri
National Institute of Technology Raipur
ckg2357@gmail.com
Debasisha
Mishra
National Institute of Technology Raipur
kapamath@gmail.com
10.22034/aot.1701-1088
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is practically very slow in many cases. Thus, works on improving the speed of the iteration scheme have attracted great interest. In this direction, comparison of the rate of convergence of the iteration schemes produced by two matrix splittings is very useful. But, in the case of matrices having many matrix splittings, this process is time-consuming. The main goal of the current article is to provide a solution to the above issue by using proper multisplittings. To this end, we propose a few comparison theorems for proper weak regular splittings and proper nonnegative splittings first. We then derive convergence and comparison theorems for proper multisplittings with the help of the theory of proper weak regular splittings.
Moore-Penrose inverse,Proper splitting,Multisplittings,Convergence theorem,Comparison theorem
http://www.aot-math.org/article_46077.html
http://www.aot-math.org/article_46077_f6ce607c8723b43d05a550013f40b6f7.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
Almost periodicity of abstract Volterra integro-differential equations
353
382
EN
Marko
Kostic
marco.s@verat.net
10.22034/aot.1701-1096
The main purpose of this paper is to investigate almost periodic properties of various classes of $(a,k)$-regularized $C$-resolvent families in Banach spaces. We contemplate the work of many other authors working in this field, giving also some original contributions and applications. In general case, $(a,k)$-regularized $C$-resolvent families under our considerations are degenerate and their subgenerators are multivalued linear operators or pairs of closed linear operators. We also consider the class of $(a,k)$-regularized $(C_{1},C_{2})$-existence and uniqueness families, where the operators $C_{1}$ and $C_{2}$ are not necessarily injective, and provide several illustrative examples of abstract Volterra integro-differential equations which do have almost periodic solutions.
abstract Volterra integro-differential equations,$(a,k)$-regularized $C$-resolvent families,multivalued linear operators,degenerate integro-differential equations,almost periodicity
http://www.aot-math.org/article_46543.html
http://www.aot-math.org/article_46543_5f3533840ce6a20babba797f183f5723.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
3
2017
07
01
A note on O-frames for operators
383
395
EN
Chander
Shekhar
Department of Mathematics
Indraprastha College for Women
University of Delhi, Delhi. India
shekhar.hilbert@gmail.com
Shiv Kumar
Kumar
Kaushik
shikk2003@yahoo.co.in
10.22034/aot.1702-1122
A sufficient condition for a boundedly complete O-frame and a necessary condition for an unconditional O-frame are given. Also, a necessary and sufficient condition for an absolute O-frame is obtained. Finally, it is proved that if two operators have an absolute O-frame, then their product also has an absolute O-frame.
Schauder frame,O-frame,Unconditional O-frame
http://www.aot-math.org/article_46574.html
http://www.aot-math.org/article_46574_040397db76510ce0e6dab09d94995a7d.pdf