Spectral sets

J. Koliha

Studia Mathematica (1997)

  • Volume: 123, Issue: 2, page 97-107
  • ISSN: 0039-3223

Abstract

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The paper studies spectral sets of elements of Banach algebras as the zeros of holomorphic functions and describes them in terms of existence of idempotents. A new decomposition theorem characterizing spectral sets is obtained for bounded linear operators.

How to cite

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Koliha, J.. "Spectral sets." Studia Mathematica 123.2 (1997): 97-107. <http://eudml.org/doc/216388>.

@article{Koliha1997,
abstract = {The paper studies spectral sets of elements of Banach algebras as the zeros of holomorphic functions and describes them in terms of existence of idempotents. A new decomposition theorem characterizing spectral sets is obtained for bounded linear operators.},
author = {Koliha, J.},
journal = {Studia Mathematica},
keywords = {spectral sets; Banach algebras; zeros of holomorphic functions; existence of idempotents},
language = {eng},
number = {2},
pages = {97-107},
title = {Spectral sets},
url = {http://eudml.org/doc/216388},
volume = {123},
year = {1997},
}

TY - JOUR
AU - Koliha, J.
TI - Spectral sets
JO - Studia Mathematica
PY - 1997
VL - 123
IS - 2
SP - 97
EP - 107
AB - The paper studies spectral sets of elements of Banach algebras as the zeros of holomorphic functions and describes them in terms of existence of idempotents. A new decomposition theorem characterizing spectral sets is obtained for bounded linear operators.
LA - eng
KW - spectral sets; Banach algebras; zeros of holomorphic functions; existence of idempotents
UR - http://eudml.org/doc/216388
ER -

References

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  1. [1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973. Zbl0271.46039
  2. [2] H. R. Dowson, Spectral Theory of Linear Operators, Academic Press, London, 1978. Zbl0384.47001
  3. [3] N. Dunford, Spectral theory I. Convergence to projections, Trans. Amer. Math. Soc. 54 (1943), 185-217. Zbl0063.01185
  4. [4] N. Dunford and J. T. Schwartz, Linear Operators I, Interscience, New York, 1957. 
  5. [5] J. E. Galé, Weakly compact homomorphisms and semigroups in Banach algebras, J. London Math. Soc. 45 (1992), 113-125. Zbl0699.46024
  6. [6] H. Heuser, Functional Analysis, Wiley, New York, 1982. 
  7. [7] M. A. Kaashoek and T. T. West, Locally Compact Semi-Algebras with Applications to Spectral Theory of Positive Operators, North-Holland Math. Stud. 9, North-Holland, Amsterdam, 1974. Zbl0288.46043
  8. [8] J. J. Koliha, Convergence of an operator series, Aequationes Math. 16 (1977), 31-35. Zbl0376.47011
  9. [9] J. J. Koliha, Isolated spectral points, Proc. Amer. Math. Soc. 124 (1996), 3417-3424. Zbl0864.46028
  10. [10] M. Mbekhta, Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), 159-175. Zbl0657.47038
  11. [11] M. Mbekhta, Sur la théorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), 621-631. 
  12. [12] C. Schmoeger, On isolated points of the spectrum of a bounded linear operator, ibid. 117 (1993), 715-719. Zbl0780.47019
  13. [13] A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, Wiley, New York, 1980. Zbl0501.46003

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