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On local automorphisms and mappings that preserve idempotents

Matej BrešarPeter Šemrl — 1995

Studia Mathematica

Let B(H) be the algebra of all bounded linear operators on a Hilbert space H. Automorphisms and antiautomorphisms are the only bijective linear mappings θ of B(H) with the property that θ(P) is an idempotent whenever P ∈ B(H) is. In case H is separable and infinite-dimensional, every local automorphism of B(H) is an automorphism.

Polynomially compact derivations on Banach algebras

Matej BrešarYuri V. Turovskii — 2009

Studia Mathematica

We consider a continuous derivation D on a Banach algebra 𝓐 such that p(D) is a compact operator for some polynomial p. It is shown that either 𝓐 has a nonzero finite-dimensional ideal not contained in the radical rad(𝓐) of 𝓐 or there exists another polynomial p̃ such that p̃(D) maps 𝓐 into rad(𝓐). A special case where Dⁿ is compact is discussed in greater detail.

Compactness conditions for elementary operators

Matej BrešarYuri V. Turovskii — 2007

Studia Mathematica

Various topics concerning compact elementary operators on Banach algebras are studied: their ranges, their coefficients, and the structure of algebras having nontrivial compact elementary operators. In the first part of the paper we consider separately elementary operators of certain simple types. In the second part we obtain our main results which deal with general elementary operators.

A Unified approach to the Structure Theory of PI-Rings and GPI-Rings

Brešar, Matej — 2012

Serdica Mathematical Journal

2010 Mathematics Subject Classification: 16R20, 16R50, 16R60, 16N60. We give short proofs, based only on basic properties of the extended centroid of a prime ring, of Martindale’s theorem on prime GPI-rings and (a strengthened version of) Posner’s theorem on prime PI-rings. * Supported by the Slovenian Research Agency (program No. P1-0288).

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