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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 glimpse at the theory of Jordan-Banach triple systems.

José M. Isidro (1989)

Revista Matemática de la Universidad Complutense de Madrid

In this article, a survey of the theory of Jordan-Banach triple systems is presented. Most of the recent relevant results in this area have been included, though no proofs are given.

Alternative noetherian Banach algebras.

M. Benslimane, N. Boudi (1997)

Extracta Mathematicae

Sinclair and Tullo [6] proved that noetherian Banach algebras are finite-dimensional. In [3], Grabiner studied noetherian Banach modules. In this paper, we are concerned with alternative noetherian Banach algebras. Combining techniques from [3] with techniques and the result from [6], we prove that every alternative noetherian Banach algebra is finite-dimensional.

Analytic properties of the spectrum in Banach Jordan Systems.

Gerald Hessenberger (1996)

Collectanea Mathematica

For Banach Jordan algebras and pairs the spectrum is proved to be related to the spectrum in a Banach algebra. Consequently, it is an analytic multifunction, upper semicontinuous with a dense G delta-set of points of continuity, and the scarcity theorem holds.

Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains

Kazimierz Włodarczyk (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in J * -algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.

Aspects of the theory of derivations

Gerard Murphy (1994)

Banach Center Publications

We survey some old and new results in the theory of derivations on Banach algebras. Although our overview is broad ranging, our principal interest is in recent results concerning conditions on a derivation implying that its range is contained in the radical of the algebra.

Asymmetric decompositions of vectors in J B * -algebras

Akhlaq A. Siddiqui (2006)

Archivum Mathematicum

By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital J B * -algebra permits that combination to be expressed as convex combination of fewer unitaries of the same algebra, we generalise various results of R. V. Kadison and G. K. Pedersen. In the sequel, we shall give a couple of characterisations of J B * -algebras of t s r 1 .

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