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

100%

Galindo A., Palacios Á.

Studia Mathematica

2005

tom 166

nr 1

83-91

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.

Unitary Banach algebras

81%

Becerra Guerrero J., Cowell S., Palacios Á., Wood G.

Studia Mathematica

2004

tom 162

nr 1

25-51

In a Banach algebra an invertible element which has norm one and whose inverse has norm one is called unitary. The algebra is unitary if the closed convex hull of the unitary elements is the closed unit ball. The main examples are the C*-algebras and the ℓ₁ group algebra of a group. In this paper, different characterizations of unitary algebras are obtained in terms of numerical ranges, dentability and holomorphy. In the process some new characterizations of C*-algebras are given.

Ograniczanie wyników

2 Studia Mathematica

2 Palacios Á.

1 Becerra Guerrero J.

1 Cowell S.

1 Galindo A.

1 Wood G.

1 2005

1 2004

Wyniki wyszukiwania

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

Unitary Banach algebras