The spectra of unbounded hyponormal operators
HTML articles powered by AMS MathViewer
- by C. R. Putnam PDF
- Proc. Amer. Math. Soc. 31 (1972), 458-464 Request permission
Abstract:
A bounded operator $T$ on a Hilbert space is said to be completely hyponormal if ${T^\ast }T - T{T^\ast } \geqq 0$ and if $T$ has no nontrivial reducing space on which it is normal. If $0$ is in the spectrum of such an operator $T$ and if the spectrum of $T$ near $0$ is not “too dense,” then the unbounded operator ${T^{ - 1}}$ acts as though it were bounded. In particular, under certain conditions, ${T^{ - 1}}$ has a rectangular representation with absolutely continuous real and imaginary parts whose spectra are the closures of the projections of the spectrum of ${T^{ - 1}}$ onto the coordinate axes.References
-
K. F. Clancey, Spectral properties of semi-normal operators, Thesis, Purdue University, Lafayette, Ind., 1969.
- C. R. Putnam, On the spectra of semi-normal operators, Trans. Amer. Math. Soc. 119 (1965), 509–523. MR 185446, DOI 10.1090/S0002-9947-1965-0185446-5
- C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag New York, Inc., New York, 1967. MR 0217618
- C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323–330. MR 270193, DOI 10.1007/BF01111839
- C. R. Putnam, Unbounded inverses of hyponormal operators, Pacific J. Math. 35 (1970), 755–762. MR 275214
- C. R. Putnam, A similarity between hyponormal and normal spectra, Illinois J. Math. 16 (1972), 695–702. MR 326462
- J. G. Stampfli, Hyponormal operators and spectral density, Trans. Amer. Math. Soc. 117 (1965), 469–476. MR 173161, DOI 10.1090/S0002-9947-1965-0173161-3
- J. G. Stampfli, Analytic extensions and spectral localization, J. Math. Mech. 16 (1966), 287–296. MR 0196500, DOI 10.1512/iumj.1967.16.16019
- Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877, DOI 10.1090/coll/015
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 458-464
- MSC: Primary 47B20
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291848-8
- MathSciNet review: 0291848