AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

Banach代数中反三角算子矩阵的Hirano逆

文章主要研究Banach代数上反三角算子矩阵的Hirano逆.假设a∈A^(H),b∈A^(sD).如果b^(D)a=0,bab^(π)=0,证明了[a 1 b 0]具有Hirano逆,进而研究了反三角算子矩阵在弱交换条件下的Hirano逆.由此获得了新的可以分解为三幂等元与幂零元和的算子矩阵.

Determinant Theory in Banach Algebras

A determinant theory is developed for Banach algebras and a characterization of those traced unital Banach algebras admitting a determinant is given.

Invariant Determinants in Banach Algebras

The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a group of trace preserving automorphisms of A.

Near-algebra和Banach代数上的特征值和不动点定理(英文)

在near-algebra和Banach代数中引入(p,q)-可加自映象f和正则可逆元的概念,得到如下的结果:在一定条件下,对于定义在near-algebra或Banach代数X中(p,q)-可加自映象f,X中的任意正则可逆元都具有公共的特征值λ=2q/(1+q),p=q≠-1.其特例就是当λ=2q/(1+q)=1时,X中的任意正则可逆元都是(p,q)-可加自映象f的不动点.

Banach代数中两个元素之和与积的广义Drazin逆

令a,b为具有单位元1的Banach代数A中两个广义Drazin逆的元素,a^(d)为a的广义Drazin逆.利用Banach代数中的幂等系统考虑两个元素之和与积的广义Drazin逆,在ab 2=bab,b^(π)ba^(2)=bπaba,a^(d)b 2=ba^(d)b等条件下给出a,b之和与积的广义Drazin逆的表达式.

Some additive results for the generalized Drazin inverse in a Banach algebra

Let a, b be two generalized Drazin invertible elements in a Banach algebra. An explicit expression for the generalized Drazin inverse of the sum a + b in terms of a,b,a^d,b^d is given. The generalized Drazin inverse for the sum of two elements in a Banach algebra is studied by means of the system of idempotents. It is first proved that a + b∈A^(qnil) under the condition that a,b∈A^(qnil),aba = 0 and ab^2= 0 and then the explicit expressions for the generalized Drazin inverse of the sum a + b under some newconditions are given. Also, some known results are extended.

FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.

APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS

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 ／ {0}.

Common Fixed Point Theorems in Non-normal Cone Metric Spaces with Banach Algebras

In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover,we give an example to support the main assertions.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

THE BANACH ALGEBRAS GENERATED BY OPERATORS WITH ONE-POINT SPECTRUM

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

A HYBRID FIXED POINT RESULT FOR LIPSCHITZ HOMOMORPHISMS ON QUASI-BANACH ALGEBRAS

We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.

An Improvement in Ordered Cone b-metric Spaces Over Banach Algebras

The purpose of this paper is to improve some famous theorems for contractive mapping from ρ(α + β) ∈ [0,1/s) to ρ(α + β) ∈ [0, 1) in ordered cone b-metric spaces over Banach algebras with coefficient s ≥ 1(ρ(x) is the spectral radius of the generalized Lipschitz constant x). Moreover, some similar improvements in ordered cone b-metric spaces are also obtained, which from α + β∈ [0,1/s) to α + β∈ [0, 1). Some examples are given to support that our new results are genuine improvements and generalizations.

A Characterization of Jacobson Radical in Γ-Banach Algebras

Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product V1rV2 in terms of the Jacobson radical for R1rL2. If V1 and V2 are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for R2rL1.

Solvability of Chandrasekhar’s Quadratic Integral Equations in Banach Algebra

In this paper, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contain various integral and functional equations that are considered in nonlinear analysis. Our considerations will be discussed in Banach algebra using a fixed point theorem instead of using the technique of measure of noncompactness. An important special case of that functional equation is Chandrasekhar’s integral equation which appears in radiative transfer, neutron transport and the kinetic theory of gases [1].

Hyperreflexivity of Operator Algebras of the Banach Space

In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.

Polynomial Spectrum of a Finite Sequencein a Banach Algebra

In this paper,we discuss that the polynomial spectrum,relative spectrum and Spectrum of a Pair of Elements are all compact,so their resolvent sets are all open.

Some Random Coincidence Point and Common Fixed Point Results in Cone Metric Spaces Over Banach Algebras

In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.

Decomposable Multipliers on a Banach Algebra

The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].