Analytic Structures and Higher Derivations on Commutative Banach Algebras (Short Communication)
JOHN BORIS MILLER (1973)
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JOHN BORIS MILLER (1973)
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This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if B is a unital commutative semisimple Banach algebra with connected character space, and T is a unital endomorphism of B, then T is quasicompact if and only if the operators Tⁿ converge in operator norm to a rank-one unital endomorphism of B. In this note the discussion is extended in two ways: we discuss endomorphisms...
W. Żelazko (1981)
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Richard Crownover (1970)
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Matthew J. Heath (2010)
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We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally,...
Dumitru D. Draghia (1995)
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W. SMAJDOR (1969)
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