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Acta Mathematica Sinica,English Series 2015年第9期31卷 1461-1474页

作者： Prakash A.DABHI Ali JABBARI Kazem HAGHNEJAD AZAR Department of Mathematics Sardar Patel University Department of Mathematics Payame Noor University Department of Mathematics University of Mohaghegh Ardabili

Let A and B be banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55（2）, 359-377 （1987）） is studied. The new version of a banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied.

关键词： banach algebra Lau product amenability weak amenability

Generalized Drazin spectrum of upper triangular matrices in banach algebras

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Frontiers of Mathematics in China 2023年第6期18卷 431-440页

作者： Yongfeng PANG Dong MA Danli ZHANG Department of Mathematics School of ScienceXi'an University of Architecture and TechnologyXi'an 710055China

Let A be a banach algebra with unit e and a,b,c∈A,Mc=(a c 0 b)∈M_(2)(A).The concepts of left and right generalized Drazin invertible of elements in a banach algebra are proposed.A generalized Drazin spectrum of is defined byσ_(gD)(α)={λ∈C:α-λe is not generalized Drazin invertible}.It is shown thatσ_(gD)(a)∪σ_(gD)(b)=σ_(gD)(M_(C))∪W_(2),where W_(g) is a union of certain holes σ_(gD) and W_(g)■σ_(gD)(a)∩σ_(gD)(b),or more *** addition,some properties of generalized Drazin spectrum of elements in a banach algebra are studied.

关键词： banach algebra generalized Drazin inverse generalized Drazin spectrum upper triangular matrices

APPROXIMATION OF ADJOINT OF A MULTIPLIER ON banach algebraS

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Acta Mathematica Scientia 2012年第2期32卷 783-792页

作者： A.Ghaffari S.Javadi H.Khodaei Department of Mathematics Semnan UniversityP.O.Box 35195-363SemnanIran

For a banach algebra A, we denote by .A＊ and .A＊＊ the first and the second duals of A respectively. Let T be a mapping from .A＊ to itself. In this article, we will investigate some stability results concerning the equations T（αf ＋ βg） -= αT（f）＋ βT（g）, T（af） = aT（f） andT（αf ＋βg）＋ T（αf - βg） =- 2α2T（f）＋ 2β2T（g） where f, g e .A＊, a ∈ A, and α,β ∈ Q ／ banach algebra.

关键词： Additive and quadratic mappings Arens products banach algebra multi-plier stability

THE banach algebraS GENERATED BY OPERATORS WITH ONE-POINT SPECTRUM

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Acta Mathematica Scientia 2011年第2期31卷 673-680页

作者： H. Seferoglu N. Simsek Department of Mathematics Faculty of Sciences Yuzuncu Yil University Department of Mathematics Faculty of Arts and Sciences Istanbul Commerce University

In this article, we present some results related to the structure of banach algebras generated by operators with one-point spectrum.

关键词： Representation group spectrum banach algebra group algebra

Generalized Derivations Acting on Multilinear Polynomials in Prime Rings and banach algebras

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Communications in Mathematics and Statistics 2016年第1期4卷 39-54页

作者： Basudeb Dhara Nurcan Argaç Department of Mathematics Belda CollegeBeldaPaschim MedinipurW.B.721424India Department of Mathematics Science FacultyEge University35100 BornovaIzmirTurkey

Let R be a prime ring of characteristic different from 2 with Utumi quotientring U and extended centroid C,F and G,the two nonzero generalized derivationsof R,I an ideal of R and f(x1,...,xn)a multilinear polynomial over C which is notcentral valued on *** F(G(f(x1,...,Xn))f(X1,...,Xn))=0 for all x1,...,Xn∈1,then one of the followings holds:(1)there exist a,b c Usuch that F(x)=ax and G(x)=bx for all x c R with ab=0;(2)there exista,b,p c U such that F(x)=ax+xb and G(x)=px for all x c R with F(p)=0and f(x1,...,xn)’is central valued on *** also obtain some related results in caseswhere R is a semiprime ring and banach algebra.

关键词： Prime ring Derivation Generalized derivation Extended centroid Utumi quotientring banach algebra

A CLASS OF ENTIRE DIRICHLET SERIES AS AN FK-SPACE AND A FRECHET SPACE

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Acta Mathematica Scientia 2013年第6期33卷 1571-1578页

作者： Niraj KUMAR Garima MANOCHA School of Applied Sciences Netaji Subhas Institute of TechnologySector 3 DwarkaNew Delhi-110078India

In the present paper we consider a class of entire functions represented by Dirichlet series whose coefficients belong to a commutative banach algebra and prove it to be a complex FK-space and a Frechet space.

关键词： Dirichlet series banach algebra FK-space Frechet space

CONVERGENCE RATES FOR A CLASS OF EVOLUTIONARY ALGORITHMS WITH ELITIST STRATEGY

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Acta Mathematica Scientia 2001年第4期21卷 531-540页

作者：丁立新康立山 State Key Lab of Software Engineering Wuhan University Wuhan 430072 China

This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in banach algebra. Under certain conditions that transition probability functions of Markov chains corresponding to evolutionary algorithms satisfy, the authors obtain the convergence rates of the exponential order. Furthermore, they also analyze the characteristics of the conditions which can be met by genetic operators and selection strategies.

关键词： convergence rate Markov chain banach algebra genetic operator elitist selection evolutionary algorithms

A NOTE ON THE REPRESENTATIONS FOR THE GENERALIZED DRAZIN INVERSE OF BLOCK MATRICES

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Acta Mathematica Scientia 2015年第6期35卷 1483-1491页

作者： Dijana MOSIC Faculty of Sciences and Mathematics University of Ni?

We present some representations for the generalized Drazin inverse of a block matrix x =[cd ab]in a banach algebra ~4 in terms of ad and （be）d under certain conditions,extending some recent result related to the generalized Drazin inverse of an anti-triangular operator matrix. Also, several particular cases of this result are considered.

关键词： generalized Drazin inverse block matrix banach algebra

BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

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Acta Mathematica Scientia 2014年第5期34卷 1655-1660页

作者： M.GRDAL M.T.GARAYEV S.SALTAN Suleyman Demirel University Department of Mathematics Department of Mathematics College of Science King Saud UniversityP.O.Box 2455 Riyadh 11451 Saudi Arabia

We investigate a basisity problem in the space =lpA（D）and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the spacelpA（D）, 1≤p《∞, by W zn=λnzn＋1, n≥0, with respect to the standard basis λzn＋1 n≥0. Applying the so-called ＂discrete Duhamel product＂ technique, it is proven that for any integer k ≥1 the sequence {（wi＋nk）-1｜W ｜Ei）knf}n≥0 is a basic sequence in Ei ：=span{zi＋n ：n≥0} equivalent to the basis {zi＋n}n≥0 if and only if fb（i） 6= 0. We also investigate a banach algebra structure for the subspaces Ei, i≥0.

关键词： basis basic sequence discrete Duhamel product banach algebra weightedshift operator

On the Operator Equation f(A)=A

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Acta Mathematica Sinica,English Series 1985年第4期1卷 327-334页

作者：陶志光 Department of Mathematics Guangxi University

1. IntroductionLet E be a non-zero complex Banaoh space, &(JET) the Banaoh algebra of all the operators from E into itself. Operator means "bounded linear operator" throughout. An operator function / from a domain (open set) D in the complex plane to @l(T￡} is said to be analytic, if for any x^E and q>￡E* (the dual space of E\ 9>(/(z)aO is analytic in the classical’sense in D ([1], p. 92). We denote by ja/B(D) the set of all the analytic operator functions from D into

关键词： Maximum Principle Operator Equation banach algebra Unique Fixed Point Ideal Space