Displaying similar documents to “On the algebras L p of locally compact groups”

How far is C₀(Γ,X) with Γ discrete from C₀(K,X) spaces?

Leandro Candido, Elói Medina Galego (2012)

Fundamenta Mathematicae

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For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the...

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.

The intersection convolution of relations and the Hahn-Banach type theorems

Árpád Száz (1998)

Annales Polonici Mathematici

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By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation...

Transitivity for linear operators on a Banach space

Bertram Yood (1999)

Studia Mathematica

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Let G be the multiplicative group of invertible elements of E(X), the algebra of all bounded linear operators on a Banach space X. In 1945 Mackey showed that if x 1 , … , x n and y 1 , … , y n are any two sets of linearly independent elements of X with the same number of items, then there exists T ∈ G so that T ( x k ) = y k , k = 1 , … , n . We prove that some proper multiplicative subgroups of G have this property.