Spectral sets

• Autorzy: J. J. Koliha
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H30: Functional calculus in topological algebras
• 47A25: Spectral sets
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 123
• Numer: 2
• Strony: 97-107

Daty

wydano

1997

otrzymano

1995-08-24

poprawiono

1996-11-18

Twórcy

autor

J. J. Koliha

• Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia

Bibliografia

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