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.


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


Zbl 0246.47006
Full Text: EuDML


[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
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[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
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