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Czasopismo
1994 | 110 | 3 | 235-250
Tytuł artykułu

On the invertibility of isometric semigroup representations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Czasopismo
Rocznik
Tom
110
Numer
3
Strony
235-250
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-08-19
Twórcy
  • St. John's College, Oxford OX1 3JP, England
  • St. Catherine's College, Oxford OX1 3UJ, England
Bibliografia
  • [1] H. Alexander, On a problem of Stolzenberg in polynomial convexity, Illinois J. Math. 22 (1978), 149-160.
  • [2] H. Alexander, Totally real sets in $C^2$, Proc. Amer. Math. Soc. 111 (1991), 131-133.
  • [3] W. Arendt and C. J. K. Batty, Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306 (1988), 837-852.
  • [4] C. J. K. Batty and Vũ Quôc Phóng, Stability of strongly continuous representations of abelian semigroups, Math. Z. (1992), 75-88.
  • [5] R. G. Douglas, On extending commutative semigroups of operators, Bull. London Math. Soc. 1 (1969), 157-159.
  • [6] Yu. I. Lyubich, Introduction to the Theory of Banach Representations of Groups, Birkhäuser, Basel, 1988.
  • [7] Yu. I. Lyubich and Vũ Quôc Phóng, Asymptotic stability of linear differential equations in Banach spaces, Studia Math. 88 (1988), 37-42.
  • [8] G. K. Pedersen, C*-algebras and their Automorphism Groups, Academic Press, London, 1979.
  • [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.
  • [11] G. M. Sklyar and V. A. Shirman, On the asymptotic stability of a linear differential equation in a Banach space, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 37 (1982), 127-132 (in Russian).
  • [12] G. Stolzenberg, Polynomially and rationally convex sets, Acta Math. 109 (1963), 259-289.
  • [13] J. Wermer, Banach Algebras and Several Complex Variables, Springer, New York, 1976.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv110i3p235bwm
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