×

Joint essential spectra. (English) Zbl 0571.47001

The notion of joint Fredholm n-tuple of closed operators with the same domain which is dense in a Hilbert space is defined. The result analogous to Atkinson’s theorem is proved and several characterizations [analogous to those in P. A. Fillmore, J. G. Stampfli and J. P. Williams, Acta. Sci. Math. 33, 179-192 (1972; Zbl 0246.47006)] are also discussed. Also Weyl’s theorem for an n-tuple of normal operators is proved.

MSC:

47A10 Spectrum, resolvent
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A53 (Semi-) Fredholm operators; index theories

Citations:

Zbl 0246.47006
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] A. T. Dash: Joint essential spectra. Pacific J. Math., 64 (1976), 119-128. · Zbl 0329.47001 · doi:10.2140/pjm.1976.64.119
[2] R. G. Douglas: Banach algebra techniques in operator theory. Acad. Press, 1972. · Zbl 0247.47001
[3] P. A. Fillmore, J. G. Stampfli, J. P. Williams: On the essential numerical range, the essential spectrum and a problem of Halmos. Acta Sci. Math. Szegal, 33 (1972), 179-192. · Zbl 0246.47006
[4] P. R. Halmos: A Hilbert space problem book. Van Nostrand-Reinhold, 1967. · Zbl 0144.38704
[5] T. Kato: Peturbation theory for linear operators. Springer Verlag, 1980.
[6] A. B. Patel: A joint spectral theorem for unbounded normal operators. J. Australian Math. Soc., (Series A) 34 (1983), 203-213. · Zbl 0523.47010 · doi:10.1017/S1446788700023235
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.