Displaying similar documents to “Polynomially compact elements of Banach algebras”

Commutators in Banach *-algebras

Bertram Yood (2008)

Studia Mathematica

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The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.

1-amenability of 𝒜(X) for Banach spaces with 1-unconditional bases

A. Blanco (2012)

Studia Mathematica

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The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property 𝔸 has in fact the property. Some further ideas on the problem of whether or not amenability...

On the weak amenability of ℬ(X)

A. Blanco (2010)

Studia Mathematica

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We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.

Banach's school and topological algebras

Wiesław Żelazko (2009)

Banach Center Publications

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We present here some evidence of the activity of Banach Lwów School of functional analysis in the field of topological algebras. We shall list several results connected with such names as Stanisław Mazur (1905-1981), Maks (Meier) Eidelheit (1910-1943), Stefan Banach (1892-1945) and Andrzej Turowicz (1904-1989) showing that if the war had not interrupted this activity we could expect more interesting results in this direction.

Constructing non-compact operators into c₀

Iryna Banakh, Taras Banakh (2010)

Studia Mathematica

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We prove that for each dense non-compact linear operator S: X → Y between Banach spaces there is a linear operator T: Y → c₀ such that the operator TS: X → c₀ is not compact. This generalizes the Josefson-Nissenzweig Theorem.