Displaying similar documents to “Finite dimensionality in socle of Banach algebras.”

Minimal incomplete norms on Banach algebras

Michael Meyer (1992)

Studia Mathematica

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We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.

Polynomially compact derivations on Banach algebras

Matej Brešar, Yuri V. Turovskii (2009)

Studia Mathematica

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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.