ORIGINAL_ARTICLE
On the weak compactness of Weak* Dunford-Pettis operators on Banach lattices
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.
http://www.aot-math.org/article_44450_933357c2224044441dc197fc6092a9d7.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
192
200
10.22034/aot.1612-1078
Weak* Dunford-Pettis operator
weakly compact operator
M-weakly compact operator
order weakly compact operator
DP* property
El Fahri
Kamal
kamalelfahri@gmail.com
true
1
Ibno Tofail University
Ibno Tofail University
Ibno Tofail University
AUTHOR
H'michane
Jawad
hm1982jad@gmail.com
true
2
Moulay Ismail University
Moulay Ismail University
Moulay Ismail University
LEAD_AUTHOR
El Kaddouri
Abdelmonim
elkaddouri.abdelmonaim@gmail.com
true
3
Ibno Tofail University
Ibno Tofail University
Ibno Tofail University
AUTHOR
Aboutafail
Moulay Othmane
aboutafail@yahoo.fr
true
4
Universite Ibn Tofail
Universite Ibn Tofail
Universite Ibn Tofail
AUTHOR
ORIGINAL_ARTICLE
Two-weight norm inequalities for the higher-order commutators of fractional integral operators
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
http://www.aot-math.org/article_44490_12d0701fe5fcfd677d8a14ebcc6ae07d.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
201
214
10.22034/aot.1612-1075
Fractional integrals
BMO
higher-order commutators
two-weight
Caiyin
Niu
niucaiyin@yahoo.com
true
1
AUTHOR
Xiaojin
Zhang
zxj800225@126.com
true
2
LEAD_AUTHOR
ORIGINAL_ARTICLE
Properties of $J$-fusion frames in Krein spaces
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.
http://www.aot-math.org/article_44491_64927e80a0e1a76256354362aa602392.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
215
227
10.22034/aot.1612-1070
Krein Space
fusion frames
J- fusion frame
Gramian operator
regular subspace
Shibashis
Karmakar
shibashiskarmakar@gmail.com
true
1
Jadavpur University
Jadavpur University
Jadavpur University
AUTHOR
Sk. Monowar
Hossein
sami_milu@yahoo.co.uk
true
2
Department of Mathematics, Aliah University, IIA/27 New Town, Kolkata - 156, W.B., India
Department of Mathematics, Aliah University, IIA/27 New Town, Kolkata - 156, W.B., India
Department of Mathematics, Aliah University, IIA/27 New Town, Kolkata - 156, W.B., India
LEAD_AUTHOR
Kallol
Paul
kalloldada@gmail.com
true
3
Jadavpur University
Jadavpur University
Jadavpur University
AUTHOR
ORIGINAL_ARTICLE
On the behavior at infinity of certain integral operator with positive kernel
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.
http://www.aot-math.org/article_44569_2d85b42ba7132b3a7409bbf38c7fbe32.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
228
236
10.22034/aot.1701-1101
integral operators
weighted Lebesgue space
behavior at infinity
convergence almost everywhere
Homaion
Roohian
homaionroohian@gmail.com
true
1
University of Applied Science and Technology
University of Applied Science and Technology
University of Applied Science and Technology
LEAD_AUTHOR
Soroosh
Mohammadi Farsani
s_mbahman@yahoo.com
true
2
AUTHOR
ORIGINAL_ARTICLE
Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
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.
http://www.aot-math.org/article_44577_1bdf44135db255e6e380484e7e83915f.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
237
256
10.22034/aot.1703-1132
Hardy-type integral inequality
weight function
equivalent form
Riemann zeta function
operator
Michael
Rassias
michail.rassias@math.uzh.ch
true
1
LEAD_AUTHOR
Bicheng
Yang
bcyang@gdei.edu.cn
true
2
AUTHOR
ORIGINAL_ARTICLE
Existence theorems for attractive points of semigroups of Bregman generalized nonspreading mappings in Banach spaces
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.
http://www.aot-math.org/article_44913_f635b05f711ebb978d7b8c937d5de88e.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
257
268
10.22034/aot.1611-1062
Bregmann attractive point
Bregman distance
generalized Bregman nonspreading mapping
Legendre function
invariant mean
Bashir
Ali
bashiralik@yahoo.com
true
1
AUTHOR
Murtala
Harbau
murtalaharbau@yahoo.com
true
2
LEAD_AUTHOR
Lawan
Yusuf
yulah121@gmail.com
true
3
AUTHOR
ORIGINAL_ARTICLE
Boundedness of multilinear integral operators and their commutators on generalized Morrey spaces
In this paper, we obtain some boundedness of multilinear Calder\'on-Zygmund Operators, multilinear fractional integral operators and their commutators on generalized Morrey Spaces.
http://www.aot-math.org/article_45124_21a043304549ed266e88cf261bd9dd56.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
269
286
10.22034/aot.1611-1051
Calder'on-Zygmund operators
commutators
fractional integral operators
weighted Morrey spaces
Panwang
Wang
panwangw@gmail.com
true
1
LEAD_AUTHOR
Zongguang
Liu
liuzg@cumtb.edu.cn
true
2
AUTHOR
ORIGINAL_ARTICLE
Semigroup homomorphisms on matrix algebras
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.
http://www.aot-math.org/article_45172_88cbac9c3a90003dba4dce5458586234.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
287
292
10.22034/aot.1702-1121
semigroup
ring
Matrix
multiplicative
Additive
unique addition
$C^*$-algebra
Bernhard
Burgstaller
bernhardburgstaller@yahoo.de
true
1
LEAD_AUTHOR
ORIGINAL_ARTICLE
Applications of ternary rings to $C^*$-algebras
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.
http://www.aot-math.org/article_45350_b879e3ece9015535fc2a911cb1f08e32.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
293
317
10.22034/aot.1612-1085
ternary rings
Morita-Rieffel equivalence
nuclear
exact
Damian
Ferraro
dferraro@unorte.edu.uy
true
1
Universidad de la Republica
Universidad de la Republica
Universidad de la Republica
LEAD_AUTHOR
Fernando
Abadie
fabadie@cmat.edu.uy
true
2
Universidad de la Republica
Universidad de la Republica
Universidad de la Republica
AUTHOR
ORIGINAL_ARTICLE
$k$th-order slant Toeplitz operators on the Fock space
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.
http://www.aot-math.org/article_46068_02a23743ff810705868374e0b4283c1b.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
318
333
10.22034/aot.1703-1133
$k$th-order slant Toeplitz operator
Fock space
Berezin transform
Shivam Kumar
Singh
shivamkumarsingh14@gmail.com
true
1
Ph. D. Scholar, Department of Mathematics, University of Delhi, Delhi, India
Ph. D. Scholar, Department of Mathematics, University of Delhi, Delhi, India
Ph. D. Scholar, Department of Mathematics, University of Delhi, Delhi, India
LEAD_AUTHOR
Anuradha
Gupta
dishna2@yahoo.in
true
2
Associate Professor, Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi-110023, India
Associate Professor, Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi-110023, India
Associate Professor, Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi-110023, India
AUTHOR
ORIGINAL_ARTICLE
Comparison results for proper multisplittings of rectangular matrices
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.
http://www.aot-math.org/article_46077_f6ce607c8723b43d05a550013f40b6f7.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
334
352
10.22034/aot.1701-1088
Moore-Penrose inverse
proper splitting
multisplittings
convergence theorem
comparison theorem
Chinmay
Giri
ckg2357@gmail.com
true
1
National Institute of Technology Raipur
National Institute of Technology Raipur
National Institute of Technology Raipur
AUTHOR
Debasisha
Mishra
kapamath@gmail.com
true
2
National Institute of Technology Raipur
National Institute of Technology Raipur
National Institute of Technology Raipur
LEAD_AUTHOR
ORIGINAL_ARTICLE
Almost periodicity of abstract Volterra integro-differential equations
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.
http://www.aot-math.org/article_46543_5f3533840ce6a20babba797f183f5723.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
353
382
10.22034/aot.1701-1096
abstract Volterra integro-differential equations
$(a
k)$-regularized $C$-resolvent families
multivalued linear operators
degenerate integro-differential equations
almost periodicity
Marko
Kostic
marco.s@verat.net
true
1
LEAD_AUTHOR
ORIGINAL_ARTICLE
A note on O-frames for operators
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.
http://www.aot-math.org/article_46574_040397db76510ce0e6dab09d94995a7d.pdf
2017-07-01T11:23:20
2018-06-24T11:23:20
383
395
10.22034/aot.1702-1122
Schauder frame
O-frame
Unconditional O-frame
Chander
Shekhar
shekhar.hilbert@gmail.com
true
1
Department of Mathematics
Indraprastha College for Women
University of Delhi, Delhi. India
Department of Mathematics
Indraprastha College for Women
University of Delhi, Delhi. India
Department of Mathematics
Indraprastha College for Women
University of Delhi, Delhi. India
AUTHOR
Shiv Kumar
Kaushik
shikk2003@yahoo.co.in
true
2
LEAD_AUTHOR