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The Generic Local Spectrum of Any Operator is The Full Spectrum |
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| Authors: | Prunaru, Bebe Putinar, Mihai |
| Affiliation: | Department of Mathematics, Indiana University Bloomington, IN 47405, USA Institute of Mathematics, Romanian Academy PO Box 1-764, 70700 Bucharest, Romania Department of Mathematics, University of California Santa Barbara, CA 93106, USA |
| Abstract: | Let T=(T1, ..., Tn) be a commuting n-tuple of bounded linearoperators acting on some complex Banach space X. We show thatif T has the single-valued extension property, then the localspectrum  T(x) coincides with the spectrum (T), for all vectorsx X, except on a set of the first Baire category. 1991 MathematicsSubject Classification 47A11, 47A13. |
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