On the invertibility of isometric semigroup representations

C. J. K. Batty; D. Greenfield

ArticleOriginal scientific text

Title

On the invertibility of isometric semigroup representations

Authors ¹, ²

Affiliations

St. John's College, Oxford OX1 3JP, England
St. Catherine's College, Oxford OX1 3UJ, England

Abstract

Let T be a representation of a suitable abelian semigroup S by isometries on a Banach space. We study the spectral conditions which will imply that T(s) is invertible for each s in S. On the way we analyse the relationship between the spectrum of T, Sp(T,S), and its unitary spectrum

S p_{u} (T, S)

. For

S = ℤ^{n}_{+}

or

ℝ^{n}_{+}

, we establish connections with polynomial convexity.

Keywords

ENG

semigroup, isometric representation, spectrum, polynomial convexity

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Title

On the invertibility of isometric semigroup representations

Affiliations

Abstract

Keywords

Bibliography