Noninvertibility preservers on Banach algebras

It is proved that a linear surjection Ф: A → B, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective.     

Questions concerning matrix algebras and invariance of spectrum

Proceedings - Mathematical Sciences - LetA andB be unital Banach algebras withA a subalgebra ofB. Denote the algebra of alln xn matrices with entries fromA byM n (A). In this paper we prove some...     

不定酉不变线性映射的刻戈及相关结果

Let A and B be unital C*-algebras, and let J ∈ A, L ∈ B be Hermitian invertible elements. For every T ∈ A and S ∈ B,define TJ(?)=J-1T*J and SL(?) =L-1S*L. Then in such a way we endow the C*-algebras A and B with indefinite structures. We characterize firstly the Jordan (J, L)-(?)-homomorphisms on C*-algebras. As applications, we further classify the bounded linear maps ?:A→B preserving (J, L)-unitary elements. When A = B(H) and B = B(K), where H and K are infinite dimensional and complete indefinite inner product spaces on real or complex fields, we prove that indefinite-unitary preserving bounded linear surjections are of the form T →UVTV-1((?)T ∈ B(H)) or T→UVT(?)V-1 ((?)T ∈ B(H)), where U ∈ B(K) is indefinite unitary and, V : H→K is generalized indefinite unitary in the first form and generalized indefinite anti-unitary in the second one. Some results on indefinite orthogonality preserving additive maps are also given.     

Additive preservers of idempotence and Jordan homorphisms between rings of square matrices

Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn（R） the ring of all n x n matrices over R. Let （Jn（R）） be the additive subgroup of Mn（R） generated additively by all idempotent matrices. Let JJ = （Jn（R）） or Mn（R）. We describe the additive preservers of idempotence from JJ to Mm（R） when 2 is a unit of R. Thereby, we also characterize the Jordan （respectively, ring and ring anti-） homomorphisms from Mn （R） to Mm （R） when 2 is a unit of R.     

Affine mappings of invertible operators

The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

     

*-偏序的广义逆特征

利用算子矩阵分块技巧和算子的广义逆研究了复Hilbert空间H上有界线性算子的*-偏序,给出了它们的一些等价刻画.     

On linear maps preserving generalized invertibility and related properties

Let H be an infinite-dimensional complex Hilbert space, B(H) be the algebra of all bounded linear operators on H. We study surjective linear maps on B(H) preserving generalized invertibility. We also investigate surjective linear maps preserving Fredholm (respectively, semi-Fredholm) operators. Our results improve those of Mbekhta, Rodman and Šemrl.     

Group inverse and core inverse in Banach and C*-algebras

Abstract

In this paper, we have focused our study on the acute perturbation of the group inverse for the elements of Banach algebra with respect to the spectral radius. We also give perturbation analysis for the core inverse in C*- algebra. The perturbation bounds for the core inverse under some conditions are presented. Additionally, this paper extends the results obtained in [11, 14].     

范畴中态射集减序的刻划

本文研究了范畴中态射集减序的刻划问题，其主要结果是：（１）证得一般范畴情形减序的十四种刻划；（２）将Ｍｉｔｒａ、Ｂａｋｓａｌａｒｙ等人的利用（１）－逆、（１，２）－逆的包含关系及平行和来刻划复矩阵减序的结果推广到素性预加法范畴与带对合的正性预加法范畴中；（３）给出了１９８０年Ｈａｒｔｗｉｇ关于半群减序刻划的一个反例，因此否定了这个刻画．     

Coloring linear orders with Rado's partial order

Let ?_R be the preorder of embeddability between countable linear orders colored with elements of Rado's partial order (a standard example of a wqo which is not a bqo). We show that ?_R has fairly high complexity with respect to Borel reducibility (e.g. if P is a Borel preorder, then P ≤_B ?_R), although its exact classification remains open. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Criteria for the single-valued metric generalized inverses of multi-valued linear operators in banach spaces

Let X, Y be Banach spaces and M be a linear subspace in X × Y = {{x, y}|x ∈ X, y ∈ Y }. We may view M as a multi-valued linear operator from X to Y by taking M (x) = {y|{x, y} ∈ M }. In this paper, we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M . The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces.     

Random spectral theorems of self-adjoint random linear operators on complete complex random inner product modules

The purpose of this article is to give two random spectral theorems of self-adjoint random linear operators on complete complex random inner product modules.     

On derivations of algebras with involution

Summary Let X be a complex Hilbert space, let L(X) be the algebra of all bounded linear operators on X, and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D: A(X) → L(X) satisfying the relation D(AA*A) = D(A) A*A + AD(A*)A + AA*D(A), for all A ∈ A(X). In this case D is of the form D(A) = AB-BA, for all A∈ A(X) and some B ∈ L(X), which means that D is a derivation. We apply this result to semisimple H*-algebras.     

Banach * 代数

Ｖ．Ｐｔáｋ［１］在有单位元的情形下详细研究了Ｂａｎａｃｈ代数．本文将推广他的结果到一般情形．特别，我们引入了可正开拓的正线性泛函，并对它进行了刻划．