The boundary of the numerical range

Lancaster, John S.

doi:10.1090/S0002-9939-1975-0372644-2

The boundary of the numerical range
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by John S. Lancaster PDF

Proc. Amer. Math. Soc. 49 (1975), 393-398 Request permission

Abstract:

This work includes two results which indicate a set theoretic relationship between the boundary of the numerical range and the essential numerical range. Several applications are derived.

References

William F. Donoghue Jr., On the numerical range of a bounded operator, Michigan Math. J. 4 (1957), 261–263. MR 96127
P. A. Fillmore, J. G. Stampfli, and J. P. Williams, On the essential numerical range, the essential spectrum, and a problem of Halmos, Acta Sci. Math. (Szeged) 33 (1972), 179–192. MR 322534

On the numerical range of compact operators on Hilbert space

Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
Stefan Hildebrandt, Über den numerischen Wertebereich eines Operators, Math. Ann. 163 (1966), 230–247 (German). MR 200725, DOI 10.1007/BF02052287

Toeplitz operators and Weyl spectra

Norberto Salinas, Operators with essentially disconnected spectrum, Acta Sci. Math. (Szeged) 33 (1972), 193–205. MR 350450
J. G. Stampfli, Extreme points of the numerical range of a hyponormal operator, Michigan Math. J. 13 (1966), 87–89. MR 187097
J. G. Stampfli and J. P. Williams, Growth conditions and the numerical range in a Banach algebra, Tohoku Math. J. (2) 20 (1968), 417–424. MR 243352, DOI 10.2748/tmj/1178243070