Properties of the spectral radius in Banach algebras
Jaroslav Zemánek (1982)
Banach Center Publications
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Displaying similar documents to “Spectral characterizations of central elements in Banach algebras”
Properties of the spectral radius in Banach algebras
A survey of recent results on the spectral radius in Banach algebras
Zemánek, Jaroslav
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A remark concerning commutativity modulo radical in Banach algebras
Pavla Vrbová (1981)
Commentationes Mathematicae Universitatis Carolinae
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Some uses of subharmonicity in functional analysis
Bernard Aupetit (1982)
Banach Center Publications
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Concerning spectral characterizations of the radical in Banach algebras
Jaroslav Zemánek (1976)
Commentationes Mathematicae Universitatis Carolinae
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Commutators of quasinilpotents and invariant subspaces
A. Katavolos, C. Stamatopoulos (1998)
Studia Mathematica
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It is proved that the set Q of quasinilpotent elements in a Banach algebra is an ideal, i.e. equal to the Jacobson radical, if (and only if) the condition [Q,Q] ⊆ Q (or a similar condition concerning anticommutators) holds. In fact, if the inner derivation defined by a quasinilpotent element p maps Q into itself then p ∈ Rad A. Higher commutator conditions of quasinilpotents are also studied. It is shown that if a Banach algebra satisfies such a condition, then every quasinilpotent element...