The essential selfcommutator of a subnormal operator
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- by John B. Conway and Nathan S. Feldman PDF
- Proc. Amer. Math. Soc. 125 (1997), 243-244 Request permission
Abstract:
In this paper an easier proof is obtained of Alexandru Aleman’s extension of an inequality of Axler and Shapiro for subnormal operators to the essential norm. The method is applied to show that a hyponormal operator whose essential spectrum has area zero must be essentially normal.References
- Jim Agler, Hypercontractions and subnormality, J. Operator Theory 13 (1985), no. 2, 203–217. MR 775993
- A. Aleman, Subnormal operators with compact selfcommutator (preprint).
- H. Alexander, Projections of polynomial hulls, J. Functional Analysis 13 (1973), 13–19. MR 0338444, DOI 10.1016/0022-1236(73)90063-3
- Sheldon Axler and Joel H. Shapiro, Putnam’s theorem, Alexander’s spectral area estimate, and VMO, Math. Ann. 271 (1985), no. 2, 161–183. MR 783550, DOI 10.1007/BF01455985
- J. W. Bunce and J. A. Deddens, On the normal spectrum of a subnormal operator, Proc. Amer. Math. Soc. 63 (1977), no. 1, 107–110. MR 435912, DOI 10.1090/S0002-9939-1977-0435912-3
- John B. Conway, The theory of subnormal operators, Mathematical Surveys and Monographs, vol. 36, American Mathematical Society, Providence, RI, 1991. MR 1112128, DOI 10.1090/surv/036
- C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323–330. MR 270193, DOI 10.1007/BF01111839
Additional Information
- John B. Conway
- Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300
- Nathan S. Feldman
- Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300
- Received by editor(s): August 15, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 243-244
- MSC (1991): Primary 47B20; Secondary 30E10
- DOI: https://doi.org/10.1090/S0002-9939-97-03698-8
- MathSciNet review: 1363417