Power-bounded elements and radical Banach algebras

• Autorzy: Graham R. Allan
• Języki publikacji: EN

Abstrakty

EN

Firstly, we give extensions of results of Gelfand, Esterle and Katznelson--Tzafriri on power-bounded operators. Secondly, some results and questions relating to power-bounded elements in the unitization of a commutative radical Banach algebra are discussed.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 38
• Numer: 1
• Strony: 9-16

Daty

wydano

1997

Twórcy

autor

Graham R. Allan

• Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, England

Bibliografia

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• [4] J. Esterle, Quasimultipliers, representations of $H^∞$, and the closed ideal problem for commutative Banach algebras, in: Radical Banach Algebras and Automatic Continuity, Proc. Conf. Long Beach 1981, J. Bachar et al. (eds.), Lecture Notes in Math. 975, Springer, Berlin, 1983, 66-162.
• [5] I. Gelfand, Zur Theorie der Charaktere der abelschen topologischen Gruppen, Rec. Math. N.S. (Mat. Sb.) 9 (51) (1941), 49-50.
• [6] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton 1967.
• [7] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I., 1957.
• [8] Y. Katznelson and L. Tzafriri, On power-bounded operators, J. Funct. Anal. 68 (1986), 313-328.
• [9] T. Pytlik, Analytic semigroups in Banach algebras, Colloq. Math. 51 (1987), 287-294.