Abstract
Some results are obtained concerning absolute continuity properties of certain selfadjoint operators. In particular, it is shown that if T is completely hyponormal with the polar factorization T = U|T|, where U is unitary, and if either its selfcommutator T*T - TT* has finite rank or U has bounded spectral multiplicity, and if, in addition, the spectrum of T is sufficiently thin near each of two distinct rays issuing from the origin, then |T| has an absolutely continuous part.
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References
C.A. Berger and B.I. Shaw, Selfcommutators of multicyclic hyponormal operators are always trace class, Bull. Amer. Math. Soc., 79 (1973), 1193–1199.
R.W. Carey and J.D. Pincus, Construction of seminormal operators with prescribed mosaic, Ind. Univ. Math. Jour., 23 (1974), 1155–1165.
K. Clancey, Seminormal operators, Lecture notes in mathematics, 742, Springer-Verlag, 1979.
P.R. Halmos, Introduction to Hilbert space, 2nd edition, Chelsea Pub. Co., 1957.
P.R. Halmos, A Hilbert space problem book, van Nostrand Co., 1967.
T. Kato, Perturbation theory for linear operators, Die Grundlehren der Math. Wiss., 132, Springer-Verlag, 1966.
T. Kato, Smooth operators and commutators, Studia Math., 3 (1968), 535–546.
C.R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Math., 36, Springer-Verlag, 1967.
C.R. Putnam, An inequality for the area of hyponormal spectra, Math. Zeits., 116 (1970), 323–330.
C.R. Putnam, Trace norm inequalities for the measure of hyponormal spectra, Ind. Univ. Math. Jour., 21 (1972), 775–779.
C.R. Putnam, The role of zero sets in the spectra of hyponormal operators, Proc. Amer. Math. Soc., 43 (1974), 137–140.
C.R. Putnam, Spectra of polar factors of hyponormal operators, Trans. Amer. Math. Soc., 188 (1974), 419–428.
C.R. Putnam, A norm inequality in hyponormal operator theory, Mich. Math. Jour., 22 (1975), 195–200.
C.R. Putnam, A polar area inequality for hyponormal spectra, Jour. Operator Theory, 4 (1980), 191–200.
C.R. Putnam, Absolute continuity of polar factors of hyponormal operators, Proceedings of Conference on Differential Equations in Analysis and Geometry in honor of Philip Hartman, Amer. Jour. Math, (to appear).
R. Schatten, Norm ideals of completely continuous operators, Springer, Berlin, 1960.
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© 1982 Springer Basel AG
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Putnam, C.R. (1982). The Spectrum of the Absolute Value of a Hyponormal Operator. In: Gohberg, I. (eds) Toeplitz Centennial. Operator Theory: Advances and Applications, vol 4. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5183-1_26
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DOI: https://doi.org/10.1007/978-3-0348-5183-1_26
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5184-8
Online ISBN: 978-3-0348-5183-1
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