Let X and Y be infinite-dimensional complex Banach spaces, and (Y) satisfies $\sigma_
{\varphi (T)\varphi (S)}(y_0)~=~\sigma_ {TS}(x_0),~(T,~ S\in {\mathcal B}(X)), $ if and only if …

Let denote the algebra of all bounded linear operators on a Banach space. Let and be
infinite-dimensional complex Banach spaces, and fix two nonzero vectors and. Then we …

Let B (X) be the algebra of all bounded linear operators on a complex Banach space X. We
give the concrete form of every unital surjective map φ on B (X) such that AB is a non-zero …

Linear maps preserving idempotency of products or triple Jordan products of operators Page
1 Linear Algebra and its Applications 429 (2008) 181–189 Available online at www.sciencedirect.com …

Abstract Let AA and BB be unital semisimple complex Banach algebras, and let\varphi_1 φ
1 and\varphi_2 φ 2 be maps from AA onto B B. We show that if the socle of AA is an …

Let M n (C) be the algebra of all n× n complex matrices, and fix a nonzero vector x 0∈ C n.
We show that a map φ from M n (C) into itself satisfies σ φ (T) φ (S)+ φ (S) φ (T)(x 0)= σ T S+ …

Local Lie derivations of nest algebras - ScienceDirect Skip to main contentSkip to article Elsevier
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Let H and K be infinite dimensional complex Hilbert spaces and let B (H) be the algebra of
all bounded linear operators on H. Let σ T (h) denote the local spectrum of an operator T∈ B …

Let B (X) be the algebra of all bounded linear operators on a complex Banach space X. For
an operator T∈ B (X), let r T (x):= lim sup n→∞∥ T nx∥ 1/n be the local spectral radius of T …

A spectral preserver is a map between Banach algebras such that some properties or
objects connected with the spectra of algebra elements are invariant under its action …