On the weak compactness of Weak* Dunford-Pettis operators on Banach lattices
El Fahri
Kamal
Ibno Tofail University
author
H'michane
Jawad
Moulay Ismail University
author
El Kaddouri
Abdelmonim
Ibno Tofail University
author
Aboutafail
Moulay Othmane
Universite Ibn Tofail
author
text
article
2017
eng
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 $T : E\longrightarrow F$ 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 $T: E\longrightarrow F$ is M-weakly compact if, and only if, the norms of $E^{\prime}$ and $F$ are order continuous or $E$ is finite-dimensional.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
192
200
http://www.aot-math.org/article_44450_933357c2224044441dc197fc6092a9d7.pdf
dx.doi.org/10.22034/aot.1612-1078
Two-weight norm inequalities for the higher-order commutators of fractional integral operators
Caiyin
Niu
author
Xiaojin
Zhang
author
text
article
2017
eng
In this paper, we obtain several sufficient conditions such that the higher-order commutators $I_{\alpha,b}^m$ generated by $I_\alpha$ and $b\in \textrm{BMO}(\mathbb{R}^n)$ is bounded from $L^p(v)$ to $L^q(u)$, where $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{n}$ and $0<\alpha<n$.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
201
214
http://www.aot-math.org/article_44490_12d0701fe5fcfd677d8a14ebcc6ae07d.pdf
dx.doi.org/10.22034/aot.1612-1075
Properties of $J$-fusion frames in Krein spaces
Shibashis
Karmakar
Jadavpur University
author
Sk. Monowar
Hossein
Department of Mathematics, Aliah University, IIA/27 New Town, Kolkata - 156, W.B., India
author
Kallol
Paul
Jadavpur University
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
215
227
http://www.aot-math.org/article_44491_64927e80a0e1a76256354362aa602392.pdf
dx.doi.org/10.22034/aot.1612-1070
On the behavior at infinity of certain integral operator with positive kernel
Homaion
Roohian
University of Applied Science and Technology
author
Soroosh
Mohammadi Farsani
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
228
236
http://www.aot-math.org/article_44569_2d85b42ba7132b3a7409bbf38c7fbe32.pdf
dx.doi.org/10.22034/aot.1701-1101
Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
Michael
Rassias
author
Bicheng
Yang
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
237
256
http://www.aot-math.org/article_44577_1bdf44135db255e6e380484e7e83915f.pdf
dx.doi.org/10.22034/aot.1703-1132
Existence theorems for attractive points of semigroups of Bregman generalized nonspreading mappings in Banach spaces
Bashir
Ali
author
Murtala
Harbau
author
Lawan
Yusuf
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
257
268
http://www.aot-math.org/article_44913_f635b05f711ebb978d7b8c937d5de88e.pdf
dx.doi.org/10.22034/aot.1611-1062
Boundedness of multilinear integral operators and their commutators on generalized Morrey spaces
Panwang
Wang
author
Zongguang
Liu
author
text
article
2017
eng
In this paper, we obtain some boundedness of multilinear Calder\'on-Zygmund Operators, multilinear fractional integral operators and their commutators on generalized Morrey Spaces.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
269
286
http://www.aot-math.org/article_45124_21a043304549ed266e88cf261bd9dd56.pdf
dx.doi.org/10.22034/aot.1611-1051
Semigroup homomorphisms on matrix algebras
Bernhard
Burgstaller
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
287
292
http://www.aot-math.org/article_45172_88cbac9c3a90003dba4dce5458586234.pdf
dx.doi.org/10.22034/aot.1702-1121
Applications of ternary rings to $C^*$-algebras
Damian
Ferraro
Universidad de la Republica
author
Fernando
Abadie
Universidad de la Republica
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
293
317
http://www.aot-math.org/article_45350_b879e3ece9015535fc2a911cb1f08e32.pdf
dx.doi.org/10.22034/aot.1612-1085
$k$th-order slant Toeplitz operators on the Fock space
Shivam Kumar
Singh
Ph. D. Scholar, Department of Mathematics, University of Delhi, Delhi, India
author
Anuradha
Gupta
Associate Professor, Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi-110023, India
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
318
333
http://www.aot-math.org/article_46068_02a23743ff810705868374e0b4283c1b.pdf
dx.doi.org/10.22034/aot.1703-1133
Comparison results for proper multisplittings of rectangular matrices
Chinmay
Giri
National Institute of Technology Raipur
author
Debasisha
Mishra
National Institute of Technology Raipur
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
334
352
http://www.aot-math.org/article_46077_f6ce607c8723b43d05a550013f40b6f7.pdf
dx.doi.org/10.22034/aot.1701-1088
Almost periodicity of abstract Volterra integro-differential equations
Marko
Kostic
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
353
382
http://www.aot-math.org/article_46543_5f3533840ce6a20babba797f183f5723.pdf
dx.doi.org/10.22034/aot.1701-1096
A note on O-frames for operators
Chander
Shekhar
Department of Mathematics
Indraprastha College for Women
University of Delhi, Delhi. India
author
Shiv Kumar
Kaushik
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
3
no.
2017
383
395
http://www.aot-math.org/article_46574_040397db76510ce0e6dab09d94995a7d.pdf
dx.doi.org/10.22034/aot.1702-1122