Boundaries of the spectra in ℒ(𝒳)

Lee, Woo Young

doi:10.1090/S0002-9939-1992-1094504-4

Boundaries of the spectra in $\mathcal {L}(X)$
HTML articles powered by AMS MathViewer

by Woo Young Lee PDF

Proc. Amer. Math. Soc. 116 (1992), 185-189 Request permission

Abstract:

Suppose $T$ is a bounded linear operator on a complex Banach space $X$. If $T$ is "regular" with some finite dimensional intersection property and if 0 is in the boundary of the spectrum of $T$ then 0 is an isolated point of it.

References

S. K. Berberian, The Weyl spectrum of an operator, Indiana Univ. Math. J. 20 (1970/71), 529–544. MR 279623, DOI 10.1512/iumj.1970.20.20044
John B. Conway, A course in functional analysis, Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1985. MR 768926, DOI 10.1007/978-1-4757-3828-5
Seymour Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0200692
Robin Harte, Regular boundary elements, Proc. Amer. Math. Soc. 99 (1987), no. 2, 328–330. MR 870795, DOI 10.1090/S0002-9939-1987-0870795-5
Robin Harte, Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics, vol. 109, Marcel Dekker, Inc., New York, 1988. MR 920812
Harro G. Heuser, Functional analysis, A Wiley-Interscience Publication, John Wiley & Sons, Ltd., Chichester, 1982. Translated from the German by John Horváth. MR 640429
Woo Young Lee, Relatively open mappings, Proc. Amer. Math. Soc. 108 (1990), no. 1, 93–94. MR 984804, DOI 10.1090/S0002-9939-1990-0984804-6
C. R. Putnam, The spectra of operators having resolvents of first-order growth, Trans. Amer. Math. Soc. 133 (1968), 505–510. MR 229073, DOI 10.1090/S0002-9947-1968-0229073-2
Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062
Albert Wilansky, Modern methods in topological vector spaces, McGraw-Hill International Book Co., New York, 1978. MR 518316