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ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, U.K.

Abstract

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.

Bibliography

  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.
Studia Mathematica
1996/121/2
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Pages:
185-192
Main language of publication
English
Received
1996-02-20
Accepted
1996-05-07
Published
1996
Exact and natural sciences