A local spectral theory for operators. V. Spectral subspaces for hyponormal operators

Stampfli, Joseph G.

doi:10.1090/S0002-9947-1976-0420325-4

A local spectral theory for operators. V. Spectral subspaces for hyponormal operators
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Trans. Amer. Math. Soc. 217 (1976), 285-296 Request permission

Abstract:

In the first part of the paper we show that the local resolvent of a hyponormal operator satisfies a rather stringent growth condition. This result enables one to show that under a mild restriction, hyponormal operators satisfy Dunford’s C condition. This in turn leads to a number of corollaries concerning invariant subspaces. In the second part we consider the local spectrum of a subnormal operator. The third section is concerned with the study of quasi-triangular hyponormal operators.

References

Some results on non-quasitriangular operators

18

48

Robert G. Bartle, Spectral localization of operators in Banach spaces, Math. Ann. 153 (1964), 261–269. MR 164243, DOI 10.1007/BF01362416
Joseph Bram, Subnormal operators, Duke Math. J. 22 (1955), 75–94. MR 68129
James E. Brennan, Invariant subspaces and rational approximation, J. Functional Analysis 7 (1971), 285–310. MR 0423059, DOI 10.1016/0022-1236(71)90036-x
Kevin F. Clancey and Bernard B. Morrel, The essential spectrum of some Toeplitz operators, Proc. Amer. Math. Soc. 44 (1974), 129–134. MR 341162, DOI 10.1090/S0002-9939-1974-0341162-9
James A. Deddens and Joseph G. Stampfli, On a question of Douglas and Fillmore, Bull. Amer. Math. Soc. 79 (1973), 327–330. MR 318937, DOI 10.1090/S0002-9904-1973-13155-6
J. Dixmier and C. Foiaş, Sur le spectre ponctuel d’un opérateur, Hilbert space operators and operator algebras (Proc. Internat. Conf., Tihany, 1970) Colloq. Math. Soc. János Bolyai, vol. 5, North-Holland, Amsterdam, 1972, pp. 127–133 (French). MR 0365175
R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. MR 203464, DOI 10.1090/S0002-9939-1966-0203464-1
Nelson Dunford, Spectral theory. II. Resolutions of the identity, Pacific J. Math. 2 (1952), 559–614. MR 51435, DOI 10.2140/pjm.1952.2.559

Linear operators

Spectral operators

P. R. Halmos, Quasitriangular operators, Acta Sci. Math. (Szeged) 29 (1968), 283–293. MR 234310

Subnormal operators and weighted shifts

C. R. Putnam, Ranges of normal and subnormal operators, Michigan Math. J. 18 (1971), 33–36. MR 276810, DOI 10.1307/mmj/1029000584
C. R. Putnam, Resolvent vectors, invariant subspaces, and sets of zero capacity, Math. Ann. 205 (1973), 165–171. MR 326428, DOI 10.1007/BF01350843
Heydar Radjavi and Peter Rosenthal, On roots of normal operators, J. Math. Anal. Appl. 34 (1971), 653–664. MR 278097, DOI 10.1016/0022-247X(71)90105-3
Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062
J. G. Stampfli, Analytic extensions and spectral localization, J. Math. Mech. 16 (1966), 287–296. MR 0196500, DOI 10.1512/iumj.1967.16.16019
Béla de Sz. Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Univ. Szeged. Sect. Sci. Math. 11 (1947), 152–157. MR 22309