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1
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Applying the density theorem for derivations to range inclusion problems

100%
Beidar K. I., Brešar M.
Studia Mathematica
|
2000
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tom 138
|
nr 1
93-100
EN
The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.
2
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Spectral characterizations of central elements in Banach algebras

100%
Brešar M., Šemrl P.
Studia Mathematica
|
1996
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tom 120
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nr 1
47-52
EN
Let A be a complex unital Banach algebra. We characterize elements belonging to Γ(A), the set of elements central modulo the radical. Our result extends and unifies several known characterizations of elements in Γ(A).
3
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On the structure of Jordan *-derivations

100%
Brešar M., Zalar B.
Colloquium Mathematicum
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1992
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tom 63
|
nr 2
163-171
4
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Polynomially compact derivations on Banach algebras

100%
Brešar M., Turovskii Y.
Studia Mathematica
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2009
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tom 190
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nr 2
185-191
EN
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.
5
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On local automorphisms and mappings that preserve idempotents

100%
Brešar M., Šemrl P.
Studia Mathematica
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1995
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tom 113
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nr 2
101-108
EN
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.
6
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Linear preservers on ℬ(X)

100%
Brešar M., Šemrl P.
Banach Center Publications
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1997
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tom 38
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nr 1
49-58
7
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A note on compact semiderivations

100%
Brešar M., Turovskii Y.
Banach Center Publications
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2005
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tom 67
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nr 1
133-137
EN
Let 𝓐 be a Banach algebra without nonzero finite dimensional ideals. Then every compact semiderivation on 𝓐 is a quasinilpotent operator mapping 𝓐 into its radical.
8
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Finite rank elements in semisimple Banach algebras

100%
Brešar M., Šemrl P.
Studia Mathematica
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1998
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tom 128
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nr 3
287-298
EN
Let A be a semisimple Banach algebra. We define the rank of a nonzero element a in the socle of A to be the minimum of the number of minimal left ideals whose sum contains a. Several characterizations of rank are proved.
9
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Compactness conditions for elementary operators

100%
Brešar M., Turovskii Y.
Studia Mathematica
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2007
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tom 178
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nr 1
1-18
EN
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.
10
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A Kleinecke-Shirokov type condition with Jordan automorphisms

81%
Brešar M., Fošner A., Fošner M.
Studia Mathematica
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2001
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tom 147
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nr 3
237-242
EN
Let φ be a Jordan automorphism of an algebra 𝓐. The situation when an element a ∈ 𝓐 satisfies $1/2(φ(a) + φ^{-1}(a)) = a$ is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson's lemma.
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