Operator spaces and similarity problems.

Pisier, Gilles

Displaying similar documents to “Operator spaces and similarity problems.”

On the uniqueness of uniform norms and C*-norms

P. A. Dabhi, H. V. Dedania (2009)

Studia Mathematica

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We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm;...

A simple example of a non-commutative Arens product.

Ignacio Zalduendo (1991)

Publicacions Matemàtiques

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A simple and natural example is given of a non-commuting Arens multiplication.

Some results on non-commutative Banach function spaces.

Keiichi Watanabe (1992)

Mathematische Zeitschrift

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Un example d'algèbre de Banach commutative radicale a unité approchée bornée sans multiplicateur non trival.

Konin Koua (1985)

Mathematica Scandinavica

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Banach Spaces Determined by Their Uniform Structures.

W.B. Johnson, J. Lindenstrauss (1996)

Geometric and functional analysis

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On a fixed-point theorem of Banach-type for uniform spaces

J. Reinermann (1969)

Matematički Vesnik

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Beurling algebras and uniform norms

S. J. Bhatt, H. V. Dedania (2004)

Studia Mathematica

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Given a locally compact abelian group G with a measurable weight ω, it is shown that the Beurling algebra L¹(G,ω) admits either exactly one uniform norm or infinitely many uniform norms, and that L¹(G,ω) admits exactly one uniform norm iff it admits a minimum uniform norm.

Quasicompact endomorphisms of commutative semiprime Banach algebras

Joel F. Feinstein, Herbert Kamowitz (2010)

Banach Center Publications

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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...