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Some Tauberian theorems related to operator theory

C. Batty — 1994

Banach Center Publications

This article is a survey of some Tauberian theorems obtained recently in connection with work on asymptotic behaviour of semigroups of operators on Banach spaces. The results in operator theory are described in [6], where we made little attempt to show the Tauberian aspects. At the end of this article, we will give a sketch of the connections between the results in this article and in [6]; for details, the reader can turn to the original papers. In this article, we make no attempt to describe...

Asymptotic behaviour of semigroups of operators

C. Batty — 1994

Banach Center Publications

On the invertibility of isometric semigroup representations

C. Batty; D. Greenfield — 1994

Studia Mathematica

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.

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Some Tauberian theorems related to operator theory

Asymptotic behaviour of semigroups of operators

On the invertibility of isometric semigroup representations