Power-bounded elements and radical Banach algebras

Graham Allan

Banach Center Publications (1997)

  • Volume: 38, Issue: 1, page 9-16
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Allan, Graham. "Power-bounded elements and radical Banach algebras." Banach Center Publications 38.1 (1997): 9-16. <http://eudml.org/doc/208651>.

@article{Allan1997,
abstract = {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.},
author = {Allan, Graham},
journal = {Banach Center Publications},
keywords = {power-bounded operators; commutative radical Banach algebra},
language = {eng},
number = {1},
pages = {9-16},
title = {Power-bounded elements and radical Banach algebras},
url = {http://eudml.org/doc/208651},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Allan, Graham
TI - Power-bounded elements and radical Banach algebras
JO - Banach Center Publications
PY - 1997
VL - 38
IS - 1
SP - 9
EP - 16
AB - 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.
LA - eng
KW - power-bounded operators; commutative radical Banach algebra
UR - http://eudml.org/doc/208651
ER -

References

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  1. [1] G. R. Allan, A. G. O'Farrell and T. J. Ransford, A tauberian theorem arising in operator theory, Bull. London Math. Soc. 19 (1987), 537-545. Zbl0652.46041
  2. [2] G. R. Allan and T. J. Ransford, Power-dominated elements in a Banach algebra, Studia Math. 94 (1989), 63-79. Zbl0705.46021
  3. [3] R. P. Boas, Entire Functions, Academic Press, New York, 1954. Zbl0058.30201
  4. [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. [5] I. Gelfand, Zur Theorie der Charaktere der abelschen topologischen Gruppen, Rec. Math. N.S. (Mat. Sb.) 9 (51) (1941), 49-50. Zbl67.0407.02
  6. [6] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton 1967. 
  7. [7] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I., 1957. Zbl0078.10004
  8. [8] Y. Katznelson and L. Tzafriri, On power-bounded operators, J. Funct. Anal. 68 (1986), 313-328. 
  9. [9] T. Pytlik, Analytic semigroups in Banach algebras, Colloq. Math. 51 (1987), 287-294. Zbl0632.46043

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