# On the invertibility of isometric semigroup representations

Studia Mathematica (1994)

- Volume: 110, Issue: 3, page 235-250
- ISSN: 0039-3223

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topBatty, C., and Greenfield, D.. "On the invertibility of isometric semigroup representations." Studia Mathematica 110.3 (1994): 235-250. <http://eudml.org/doc/216111>.

@article{Batty1994,

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

author = {Batty, C., Greenfield, D.},

journal = {Studia Mathematica},

keywords = {semigroup; isometric representation; spectrum; polynomial convexity; representation of a suitable Abelian semigroup; isometries on a Banach space; spectral conditions; unitary spectrum},

language = {eng},

number = {3},

pages = {235-250},

title = {On the invertibility of isometric semigroup representations},

url = {http://eudml.org/doc/216111},

volume = {110},

year = {1994},

}

TY - JOUR

AU - Batty, C.

AU - Greenfield, D.

TI - On the invertibility of isometric semigroup representations

JO - Studia Mathematica

PY - 1994

VL - 110

IS - 3

SP - 235

EP - 250

AB - 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.

LA - eng

KW - semigroup; isometric representation; spectrum; polynomial convexity; representation of a suitable Abelian semigroup; isometries on a Banach space; spectral conditions; unitary spectrum

UR - http://eudml.org/doc/216111

ER -

## References

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- [9] Vũ Quôc Phóng and Yu. I. Lyubich, A spectral criterion for asymptotic almost periodicity for uniformly continuous representations of abelian semigroups, Teor. Funktsiǐ Funktsional. Anal. i Prilozhen. 50 (1988), 38-43 (in Russian); English transl.: J. Soviet Math. 49 (1990), 1263-1266.
- [10] W. Rudin, Fourier Analysis on Groups, Wiley, New York, 1962. Zbl0107.09603
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- [13] J. Wermer, Banach Algebras and Several Complex Variables, Springer, New York, 1976. Zbl0336.46055

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