2017
2
3
5
204
On the weak compactness of Weak* DunfordPettis operators on Banach lattices
2
2
We characterize Banach lattices on which each positive weak* DunfordPettis operator is weakly (resp., Mweakly, resp., order weakly) compact. More precisely, we prove that if $F$ is a Banach lattice with order continuous norm, then each positive weak* DunfordPettis 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* DunfordPettis operator $T: Elongrightarrow F$ is Mweakly compact if, and only if, the norms of $E^{prime}$ and $F$ are order continuous or $E$ is finitedimensional.
1

192
200


El Fahri
Kamal
Ibno Tofail University
Ibno Tofail University
Morocco
kamalelfahri@gmail.com


H'michane
Jawad
Moulay Ismail University
Moulay Ismail University
Morocco
hm1982jad@gmail.com


El Kaddouri
Abdelmonim
Ibno Tofail University
Ibno Tofail University
Morocco
elkaddouri.abdelmonaim@gmail.com


Aboutafail
Moulay Othmane
Universite Ibn Tofail
Universite Ibn Tofail
Morocco
aboutafail@yahoo.fr
Weak* DunfordPettis operator
weakly compact operator
Mweakly compact operator
order weakly compact operator
DP* property
Twoweight norm inequalities for the higherorder commutators of fractional integral operators
2
2
In this paper, we obtain several sufficient conditions such that the higherorder 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 $0<alpha<n$.
1

201
214


Caiyin
Niu
China
niucaiyin@yahoo.com


Xiaojin
Zhang
China
zxj800225@126.com
Fractional integrals
BMO
higherorder commutators
twoweight
Properties of $J$fusion frames in Krein spaces
2
2
In this article we introduce the notion of $J$Parseval fusion frames in a Krein space $mathbb{K}$ and characterize 1uniform $J$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.
1

215
227


Shibashis
Karmakar
Jadavpur University
Jadavpur University
India
shibashiskarmakar@gmail.com


Sk. Monowar
Hossein
Department of Mathematics, Aliah University, IIA/27 New Town, Kolkata  156, W.B., India
Department of Mathematics, Aliah University,
India
sami_milu@yahoo.co.uk


Kallol
Paul
Jadavpur University
Jadavpur University
India
kalloldada@gmail.com
Krein Space
fusion frames
J fusion frame
Gramian operator
regular subspace
On the behavior at infinity of certain integral operator with positive kernel
2
2
Let $alpha>0$ and $gamma>0$. We consider integral operator of the form$${mathcal{G}}_{phi_gamma}f(x):=frac{1}{Psi_gamma (x)}int_0^x (1frac{y}{x})^{alpha1}phi_gamma(y) f(y)dy,,,,, x>0.$$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.
1

228
236


Homaion
Roohian
University of Applied Science and Technology
University of Applied Science and Technology
Iran
homaionroohian@gmail.com


Soroosh
Mohammadi Farsani
Iran
s_mbahman@yahoo.com
integral operators
weighted Lebesgue space
behavior at infinity
convergence almost everywhere
Equivalent conditions of a Hardytype integral inequality related to the extended Riemann zeta function
2
2
By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardytype integral inequality with a nonhomogeneous 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 Hardytype integral inequalities with the homogeneous kernel are deduced. We also consider the operator expressions.
1

237
256


Michael
Rassias
Switzerland
michail.rassias@math.uzh.ch


Bicheng
Yang
China
bcyang@gdei.edu.cn
Hardytype integral inequality
weight function
equivalent form
Riemann zeta function
operator
Existence theorems for attractive points of semigroups of Bregman generalized nonspreading mappings in Banach spaces
2
2
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.
1

257
268


Bashir
Ali
Nigeria
bashiralik@yahoo.com


Murtala
Harbau
Nigeria
murtalaharbau@yahoo.com


Lawan
Yusuf
Nigeria
yulah121@gmail.com
Bregmann attractive point
Bregman distance
generalized Bregman nonspreading mapping
Legendre function
invariant mean
Boundedness of multilinear integral operators and their commutators on generalized Morrey spaces
2
2
In this paper, we obtain some boundedness of multilinear Calder'onZygmund Operators, multilinear fractional integral operators and their commutators on generalized Morrey Spaces.
1

269
286


Panwang
Wang
China
panwangw@gmail.com


Zongguang
Liu
Iran
liuzg@cumtb.edu.cn
Calder'onZygmund operators
commutators
fractional integral operators
weighted Morrey spaces
Semigroup homomorphisms on matrix algebras
2
2
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.
1

287
292


Bernhard
Burgstaller
Austria
bernhardburgstaller@yahoo.de
semigroup
ring
Matrix
multiplicative
Additive
unique addition
$C^*$algebra
Applications of ternary rings to $C^*$algebras
2
2
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 MoritaRieffel equivalence results between crosssectional $C^*$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 MoritaRieffel equivalence of $C^*$algebras.
1

293
317


Damian
Ferraro
Universidad de la Republica
Universidad de la Republica
Uruguay
dferraro@unorte.edu.uy


Fernando
Abadie
Universidad de la Republica
Universidad de la Republica
Uruguay
fabadie@cmat.edu.uy
ternary rings
MoritaRieffel equivalence
nuclear
exact
$k$thorder slant Toeplitz operators on the Fock space
2
2
The notion of slant Toeplitz operators $B_phi$ and $k$thorder 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 $k$thorder slant Toeplitz operators with coanalytic and harmonic symbols is discussed.
1

318
333


Shivam Kumar
Singh
Ph. D. Scholar, Department of Mathematics, University of Delhi, Delhi, India
Ph. D. Scholar, Department of Mathematics,
India
shivamkumarsingh14@gmail.com


Anuradha
Gupta
Associate Professor, Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi110023, India
Associate Professor, Department of Mathematics,
India
dishna2@yahoo.in
$k$thorder slant Toeplitz operator
Fock space
Berezin transform
Comparison results for proper multisplittings of rectangular matrices
2
2
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 timeconsuming. 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.
1

334
352


Chinmay
Giri
National Institute of Technology Raipur
National Institute of Technology Raipur
India
ckg2357@gmail.com


Debasisha
Mishra
National Institute of Technology Raipur
National Institute of Technology Raipur
India
kapamath@gmail.com
MoorePenrose inverse
proper splitting
multisplittings
convergence theorem
comparison theorem
Almost periodicity of abstract Volterra integrodifferential equations
2
2
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 integrodifferential equations which do have almost periodic solutions.
1

353
382


Marko
Kostic
Serbia
marco.s@verat.net
abstract Volterra integrodifferential equations
$(a
k)$regularized $C$resolvent families
multivalued linear operators
degenerate integrodifferential equations
almost periodicity
A note on Oframes for operators
2
2
A sufficient condition for a boundedly complete Oframe and a necessary condition for an unconditional Oframe are given. Also, a necessary and sufficient condition for an absolute Oframe is obtained. Finally, it is proved that if two operators have an absolute Oframe, then their product also has an absolute Oframe.
1

383
395


Chander
Shekhar
Department of Mathematics
Indraprastha College for Women
University of Delhi, Delhi. India
Department of Mathematics
Indraprastha College
India
shekhar.hilbert@gmail.com


Shiv Kumar
Kaushik
India
shikk2003@yahoo.co.in
Schauder frame
Oframe
Unconditional Oframe