Norm conditions on resolvents of similarities of Hilbert space operators and applications to direct sums and integrals of operators
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- by Frank Gilfeather PDF
- Proc. Amer. Math. Soc. 68 (1978), 44-48 Request permission
Abstract:
Similarities of an operator T are determined so that on certain sets the norm of the resolvents of the similarity satisfy bounding conditions independent of T. The results are applied to show that direct sums and integrals of operators are quasi-similar to operators with spectrum depending only on the spectrum of the summands.References
- Constantin Apostol, Operators quasisimilar to a normal operator, Proc. Amer. Math. Soc. 53 (1975), no. 1, 104–106. MR 402522, DOI 10.1090/S0002-9939-1975-0402522-1 D. Herrero, Quasi-similar operators with different spectra, Notices Amer. Math. Soc. 24 (1977), A-11.
- Gian-Carlo Rota, On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469–472. MR 112040, DOI 10.1002/cpa.3160130309
- J. T. Schwartz, $W^{\ast }$-algebras, Gordon and Breach Science Publishers, New York-London-Paris, 1967. MR 0232221
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 44-48
- MSC: Primary 47A10; Secondary 47A60
- DOI: https://doi.org/10.1090/S0002-9939-1978-0475583-4
- MathSciNet review: 475583