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Pointwise absolutely convergent series of operators and related classes of Banach spaces

Liudmyla Kadets, Vladimir Kadets (2012)

Open Mathematics

We study classes of operators represented as a pointwise absolutely convergent series of simpler ones, starting with rank 1 operators. In this short note we address the question, how far the repetition of this procedure can lead.

Polynomially compact derivations on Banach algebras

Matej Brešar, Yuri 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.

Produits tensoriels d'espaces de Banach et classes d'applications linéaires

Pierre Saphar (1970)

Studia Mathematica

Displaying 1 – 3 of 3

Pointwise absolutely convergent series of operators and related classes of Banach spaces

Polynomially compact derivations on Banach algebras

Produits tensoriels d'espaces de Banach et classes d'applications linéaires

Currently displaying 1 – 3 of 3