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.

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.

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.

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

Let a, b be two generalized Drazin invertibleelements in a Banach algebra. An explicit expression for thegeneralized Drazin inverse of the sum a ＋ b in terms of a, b,as, bd is given. The generalized Drazin inverse for the sum oftwo elements in a Banach algebra is studied by means of thesystem of idempotents. It is first proved that a ＋ b ∈ Aqnll underthe condition that a, b ∈ Aqnil, aba = 0 and ab^2 = 0 and then theexplicit expressions for the generalized Drazin inverse of thesum a ＋ b under some new conditions are given. Also, someknown results are extended.

ISOMETRIC ISOMORPHISMS OF TRIANGULAR BANACH ALGEBRAS

Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.

Polynomial Spectrum of a Finite Sequencein a Banach Algebra

在这份报纸，我们讨论一双元素的多项式光谱，相对光谱和光谱都是紧缩的，他们的溶剂集合都因此是开的。

Decomposable Multipliers on a Banach Algebra

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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].

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.

Generalized Drazin spectrum of upper triangular matrices in Banach algebras

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 finely.In addition,some properties of generalized Drazin spectrum of elements in a Banach algebra are studied.

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.

Homomorphisms in Quasi-Banach Algebras Associated with a Pexiderized Cauchy-Jensen Functional Equation

In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.

A Characterization of Homomorphisms Between Banach Algebras

We show that every unital invertibility preserving linear map from a von Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to a problem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simple complex Banach algebra onto another,we also show that the following statements are equivalent:(1) Φ is an homomorphism;(2)Φ is completely invertibility preserving;(3)Φ is 2-invertibility preserving.

Projections onto Invariant Subspaces of Some Banach Algebras

In this paper, among other things, the author studies the weak^＊-closed left translation invariant complemented subspace of semigroup algebras and group algebras. Also, the author studies the relationships between projections and amenability.