eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
192
200
10.22034/aot.1612-1078
44450
On the weak compactness of Weak* Dunford-Pettis operators on Banach lattices
El Fahri Kamal
kamalelfahri@gmail.com
1
H'michane Jawad
hm1982jad@gmail.com
2
El Kaddouri Abdelmonim
elkaddouri.abdelmonaim@gmail.com
3
Aboutafail Moulay Othmane
aboutafail@yahoo.fr
4
Ibno Tofail University
Moulay Ismail University
Ibno Tofail University
Universite Ibn Tofail
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.
http://www.aot-math.org/article_44450_933357c2224044441dc197fc6092a9d7.pdf
Weak* Dunford-Pettis operator
weakly compact operator
M-weakly compact operator
order weakly compact operator
DP* property
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
201
214
10.22034/aot.1612-1075
44490
Two-weight norm inequalities for the higher-order commutators of fractional integral operators
Caiyin Niu
niucaiyin@yahoo.com
1
Xiaojin Zhang
zxj800225@126.com
2
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 $0<alpha<n$.
http://www.aot-math.org/article_44490_12d0701fe5fcfd677d8a14ebcc6ae07d.pdf
Fractional integrals
BMO
higher-order commutators
two-weight
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
215
227
10.22034/aot.1612-1070
44491
Properties of $J$-fusion frames in Krein spaces
Shibashis Karmakar
shibashiskarmakar@gmail.com
1
Sk. Monowar Hossein
sami_milu@yahoo.co.uk
2
Kallol Paul
kalloldada@gmail.com
3
Jadavpur University
Department of Mathematics, Aliah University, IIA/27 New Town, Kolkata - 156, W.B., India
Jadavpur University
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
Krein Space
fusion frames
J- fusion frame
Gramian operator
regular subspace
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
228
236
10.22034/aot.1701-1101
44569
On the behavior at infinity of certain integral operator with positive kernel
Homaion Roohian
homaionroohian@gmail.com
1
Soroosh Mohammadi Farsani
s_mbahman@yahoo.com
2
University of Applied Science and Technology
Let $alpha>0$ and $gamma>0$. We consider integral operator of the form<br />$$<br />{mathcal{G}}_{phi_gamma}f(x):=frac{1}{Psi_gamma (x)}int_0^x (1-frac{y}{x})^{alpha-1}phi_gamma(y) f(y)dy,,,,, x>0.<br />$$<br />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
integral operators
weighted Lebesgue space
behavior at infinity
convergence almost everywhere
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
237
256
10.22034/aot.1703-1132
44577
Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
Michael Rassias
michail.rassias@math.uzh.ch
1
Bicheng Yang
bcyang@gdei.edu.cn
2
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
Hardy-type integral inequality
weight function
equivalent form
Riemann zeta function
operator
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
257
268
10.22034/aot.1611-1062
44913
Existence theorems for attractive points of semigroups of Bregman generalized nonspreading mappings in Banach spaces
Bashir Ali
bashiralik@yahoo.com
1
Murtala Harbau
murtalaharbau@yahoo.com
2
Lawan Yusuf
yulah121@gmail.com
3
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
Bregmann attractive point
Bregman distance
generalized Bregman nonspreading mapping
Legendre function
invariant mean
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
269
286
10.22034/aot.1611-1051
45124
Boundedness of multilinear integral operators and their commutators on generalized Morrey spaces
Panwang Wang
panwangw@gmail.com
1
Zongguang Liu
liuzg@cumtb.edu.cn
2
In this paper, we obtain some boundedness of multilinear Calder'on-Zygmund Operators, multilinear fractional integral operators and their commutators on generalized Morrey Spaces.<br /><br />
http://www.aot-math.org/article_45124_21a043304549ed266e88cf261bd9dd56.pdf
Calder'on-Zygmund operators
commutators
fractional integral operators
weighted Morrey spaces
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
287
292
10.22034/aot.1702-1121
45172
Semigroup homomorphisms on matrix algebras
Bernhard Burgstaller
bernhardburgstaller@yahoo.de
1
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
semigroup
ring
Matrix
multiplicative
Additive
unique addition
$C^*$-algebra
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
293
317
10.22034/aot.1612-1085
45350
Applications of ternary rings to $C^*$-algebras
Damian Ferraro
dferraro@unorte.edu.uy
1
Fernando Abadie
fabadie@cmat.edu.uy
2
Universidad de la Republica
Universidad de la Republica
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
ternary rings
Morita-Rieffel equivalence
nuclear
exact
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
318
333
10.22034/aot.1703-1133
46068
$k$th-order slant Toeplitz operators on the Fock space
Shivam Kumar Singh
shivamkumarsingh14@gmail.com
1
Anuradha Gupta
dishna2@yahoo.in
2
Ph. D. Scholar, Department of Mathematics, University of Delhi, Delhi, India
Associate Professor, Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi-110023, India
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.<br /><br />
http://www.aot-math.org/article_46068_02a23743ff810705868374e0b4283c1b.pdf
$k$th-order slant Toeplitz operator
Fock space
Berezin transform
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
334
352
10.22034/aot.1701-1088
46077
Comparison results for proper multisplittings of rectangular matrices
Chinmay Giri
ckg2357@gmail.com
1
Debasisha Mishra
kapamath@gmail.com
2
National Institute of Technology Raipur
National Institute of Technology Raipur
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
Moore-Penrose inverse
proper splitting
multisplittings
convergence theorem
comparison theorem
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
353
382
10.22034/aot.1701-1096
46543
Almost periodicity of abstract Volterra integro-differential equations
Marko Kostic
marco.s@verat.net
1
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
abstract Volterra integro-differential equations
$(a
k)$-regularized $C$-resolvent families
multivalued linear operators
degenerate integro-differential equations
almost periodicity
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-07-01
2
3
383
395
10.22034/aot.1702-1122
46574
A note on O-frames for operators
Chander Shekhar
shekhar.hilbert@gmail.com
1
Shiv Kumar Kaushik
shikk2003@yahoo.co.in
2
Department of Mathematics Indraprastha College for Women University of Delhi, Delhi. India
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
Schauder frame
O-frame
Unconditional O-frame