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

A. Blanco (2012)

Studia Mathematica

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 (in...

2-normed Algebras-I

Neeraj Srivastava, S. Bhattacharya, S. N. Lal (2010)

Publications de l'Institut Mathématique

2-normed Algebras-II

Neeraj Srivastava, S. Bhattacharya, S. N. Lal (2011)

Publications de l'Institut Mathématique

A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces

Antonio Moreno Galindo, Ángel Rodríguez Palacios (2005)

Studia Mathematica

We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ C(X) is equivalent to the uncountability of X. This is derived from a bilinear version of Holsztyński's theorem [3] on isometries of C(X)-spaces, which is also proved in the paper.

A characterization of characters in complex m-pseudoconvex algebras

W. Żelazko (2005)

Banach Center Publications

In this paper we extend the characterization of characters given in [1], [2] and [8] onto m-pseudoconvex algebras. As a consequence (and a generalization) we give a characterization of continuous homomorphisms from m-pseudoconvex algebras into commutative semisimple m-pseudoconvex algebras.

A characterization of maximal regular ideals in lmc algebras

Maria Fragoulopoulou (1992)

Studia Mathematica

A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.

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