2018-04-22T03:23:59Z
http://www.aot-math.org/?_action=export&rf=summon&issue=5212
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
On the weak compactness of Weak* Dunford-Pettis operators on Banach lattices
El Fahri
Kamal
H'michane
Jawad
El Kaddouri
Abdelmonim
Aboutafail
Moulay Othmane
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
2017
07
01
192
200
http://www.aot-math.org/article_44450_933357c2224044441dc197fc6092a9d7.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Two-weight norm inequalities for the higher-order commutators of fractional integral operators
Caiyin
Niu
Xiaojin
Zhang
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
2017
07
01
201
214
http://www.aot-math.org/article_44490_12d0701fe5fcfd677d8a14ebcc6ae07d.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Properties of $J$-fusion frames in Krein spaces
Shibashis
Karmakar
Sk. Monowar
Hossein
Kallol
Paul
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
2017
07
01
215
227
http://www.aot-math.org/article_44491_64927e80a0e1a76256354362aa602392.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
On the behavior at infinity of certain integral operator with positive kernel
Homaion
Roohian
Soroosh
Mohammadi Farsani
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
2017
07
01
228
236
http://www.aot-math.org/article_44569_2d85b42ba7132b3a7409bbf38c7fbe32.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
Michael
Rassias
Bicheng
Yang
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
2017
07
01
237
256
http://www.aot-math.org/article_44577_1bdf44135db255e6e380484e7e83915f.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Existence theorems for attractive points of semigroups of Bregman generalized nonspreading mappings in Banach spaces
Bashir
Ali
Murtala
Harbau
Lawan
Yusuf
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
2017
07
01
257
268
http://www.aot-math.org/article_44913_f635b05f711ebb978d7b8c937d5de88e.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Boundedness of multilinear integral operators and their commutators on generalized Morrey spaces
Panwang
Wang
Zongguang
Liu
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
2017
07
01
269
286
http://www.aot-math.org/article_45124_21a043304549ed266e88cf261bd9dd56.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Semigroup homomorphisms on matrix algebras
Bernhard
Burgstaller
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
2017
07
01
287
292
http://www.aot-math.org/article_45172_88cbac9c3a90003dba4dce5458586234.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Applications of ternary rings to $C^*$-algebras
Damian
Ferraro
Fernando
Abadie
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
2017
07
01
293
317
http://www.aot-math.org/article_45350_b879e3ece9015535fc2a911cb1f08e32.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
$k$th-order slant Toeplitz operators on the Fock space
Shivam Kumar
Singh
Anuradha
Gupta
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
2017
07
01
318
333
http://www.aot-math.org/article_46068_02a23743ff810705868374e0b4283c1b.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Comparison results for proper multisplittings of rectangular matrices
Chinmay
Giri
Debasisha
Mishra
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
2017
07
01
334
352
http://www.aot-math.org/article_46077_f6ce607c8723b43d05a550013f40b6f7.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
Almost periodicity of abstract Volterra integro-differential equations
Marko
Kostic
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
2017
07
01
353
382
http://www.aot-math.org/article_46543_5f3533840ce6a20babba797f183f5723.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
3
A note on O-frames for operators
Chander
Shekhar
Shiv Kumar
Kaushik
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
2017
07
01
383
395
http://www.aot-math.org/article_46574_040397db76510ce0e6dab09d94995a7d.pdf