# Power-bounded elements and radical Banach algebras

Banach Center Publications (1997)

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

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topAllan, 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

top- [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] G. R. Allan and T. J. Ransford, Power-dominated elements in a Banach algebra, Studia Math. 94 (1989), 63-79. Zbl0705.46021
- [3] R. P. Boas, Entire Functions, Academic Press, New York, 1954. Zbl0058.30201
- [4] J. Esterle, Quasimultipliers, representations of ${H}^{\infty}$, 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. Zbl67.0407.02
- [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. Zbl0078.10004
- [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. Zbl0632.46043

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