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

Studia Mathematica (1996)

- Volume: 121, Issue: 2, page 185-192
- ISSN: 0039-3223

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topAllan, Graham. "Sums of idempotents and a lemma of N. J. Kalton." Studia Mathematica 121.2 (1996): 185-192. <http://eudml.org/doc/216350>.

@article{Allan1996,

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.},

author = {Allan, Graham},

journal = {Studia Mathematica},

keywords = {lemma of Gelfand-Hille type; sums of idempotents},

language = {eng},

number = {2},

pages = {185-192},

title = {Sums of idempotents and a lemma of N. J. Kalton},

url = {http://eudml.org/doc/216350},

volume = {121},

year = {1996},

}

TY - JOUR

AU - Allan, Graham

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

JO - Studia Mathematica

PY - 1996

VL - 121

IS - 2

SP - 185

EP - 192

AB - 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.

LA - eng

KW - lemma of Gelfand-Hille type; sums of idempotents

UR - http://eudml.org/doc/216350

ER -

## References

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- [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] H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere of Banach algebras, Ann. of Math. 62 (1955), 217-229. Zbl0067.35002
- [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. Zbl0207.44802
- [6] J. Esterle, Quasi-multipliers, representations of ${H}^{\infty}$, 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. Zbl67.0407.02
- [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. Zbl0061.25305
- [9] N. J. Kalton, Sums of idempotents in Banach algebras, Canad. Math. Bull. 31 (1988), 448-451. Zbl0679.46033
- [10] Y. Katznelson and L. Tzafriri, On power-bounded operators, J. Funct. Anal. 68 (1986), 313-328. Zbl0611.47005
- [11] G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961), 679-698. Zbl0101.09503
- [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). Zbl0039.33601
- [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. Zbl0822.47005

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