Invariant subspaces of infinite codimension for some nonnormal operators
HTML articles powered by AMS MathViewer
- by Kevin Clancey PDF
- Proc. Amer. Math. Soc. 37 (1973), 525-528 Request permission
Abstract:
Let $\varphi \in C’[ - 1,1]$. For $f \in {L^2}( - 1,1)$ define \[ {T_\varphi }f(s) = sf(s) + \frac {{\varphi (s)}}{\pi }\int _{ - 1}^{1 \ast } {\frac {{\bar \varphi f(t)}}{{s - t}}dt.} \] Our main result says ${T_\varphi }$ has invariant subspaces of infinite co-dimension.References
-
K. F. Clancey, On the subnormality of some singular integral operators (preprint).
- Kevin Clancey, Seminormal operators with compact self-commutators, Proc. Amer. Math. Soc. 26 (1970), 447–454. MR 265976, DOI 10.1090/S0002-9939-1970-0265976-5
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
- C. R. Putnam, The spectra of semi-normal singular integral operators, Canadian J. Math. 22 (1970), 134–150. MR 259680, DOI 10.4153/CJM-1970-017-7
- C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323–330. MR 270193, DOI 10.1007/BF01111839
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
- J. Schwartz, Some results on the spectra and spectral resolutions of a class of singular integral operators, Comm. Pure Appl. Math. 15 (1962), 75–90. MR 163177, DOI 10.1002/cpa.3160150106
- A. L. Shields and L. J. Wallen, The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1970/71), 777–788. MR 287352, DOI 10.1512/iumj.1971.20.20062
- Joseph G. Stampfli, Hyponormal operators, Pacific J. Math. 12 (1962), 1453–1458. MR 149282
- 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 F. G. Tricomi, Integral equations, Interscience, New York, 1968.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 525-528
- MSC: Primary 47B20; Secondary 45E05, 47A15
- DOI: https://doi.org/10.1090/S0002-9939-1973-0308841-X
- MathSciNet review: 0308841