On the invertibility of isometric semigroup representations

Tom 110 / 1994

C. J. K. Batty Studia Mathematica 110 (1994), 235-250 DOI: 10.4064/sm-110-3-235-250


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 $Sp_{u}(T,S)$. For $S = ℤ^{n}_{+}$ or $ℝ^{n}_{+}$, we establish connections with polynomial convexity.


  • C. J. K. Batty

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