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1996 | 121 | 2 | 185-192
Tytuł artykułu

Sums of idempotents and a lemma of N. J. Kalton

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Abstrakty
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A lemma of Gelfand-Hille type is proved. It is used to give an improved version of a result of Kalton on sums of idempotents.
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Twórcy
  • Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, U.K. , G.R.Allan@pmms.cam.ac.uk
Bibliografia
  • [1] G. R. Allan, Power-bounded elements in a Banach algebra and a theorem of Gelfand, in: Conf. on Automatic Continuity and Banach Algebras (Canberra, January 1989), R. J. Loy (ed.), Proc. Centre Math. Anal. Austral. Nat. Univ. 21, Canberra, 1989, 1-12.
  • [2] G. R. Allan and T. J. Ransford, Power-dominated elements in a Banach algebra, Studia Math. 94 (1989), 63-79.
  • [3] R. P. Boas, Entire Functions, Academic Press, New York, 1954.
  • [4] H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere of Banach algebras, Ann. of Math. 62 (1955), 217-229.
  • [5] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Ser. 2, Cambridge Univ. Press, 1971.
  • [6] J. Esterle, Quasi-multipliers, representations of $H^∞$, and the closed ideal problem for commutative Banach algebras, in: Radical Banach Algebras and Automatic Continuity, Lecture Notes in Math. 975, Springer, 1983, 66-162.
  • [7] I. Gelfand, Zur Theorie der Charaktere der abelschen topologischen Gruppen, Rec. Math. N.S. (Mat. Sb.) 9 (51) (1941), 49-50.
  • [8] E. Hille, On the theory of characters of groups and semigroups in normed vector rings, Proc. Nat. Acad. Sci. U.S.A. 30 (1944), 58-60.
  • [9] N. J. Kalton, Sums of idempotents in Banach algebras, Canad. Math. Bull. 31 (1988), 448-451.
  • [10] Y. Katznelson and L. Tzafriri, On power-bounded operators, J. Funct. Anal. 68 (1986), 313-328.
  • [11] G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961), 679-698.
  • [12] G. E. Shilov, On a theorem of I. M. Gel'fand and its generalizations, Dokl. Akad. Nauk SSSR 72 (1950), 641-644 (in Russian).
  • [13] J. Zemánek, On the Gelfand-Hille theorems, in: Functional Analysis and Operator Theory, Banach Center Publ. 30, Inst. Math., Polish Acad. Sci. Warszawa, 1994, 369-385.
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bwmeta1.element.bwnjournal-article-smv121i2p185bwm
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