The joint spectrum of commuting nonnormal operators
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- by John Bunce
- Proc. Amer. Math. Soc. 29 (1971), 499-505
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283602-7
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Abstract:
We define the joint approximate spectrum of a finite family of bounded commuting operators on a Hilbert space and show that it is closed and nonempty. If the operators are all hyponormal, then the family need not be finite, and the joint approximate spectrum can be defined in terms of the multiplicative linear functionals on the generated ${C^\ast }$-algebra. These definitions extend the usual definition of the joint spectrum of a family of commuting normal operators.References
- Arlen Brown, On a class of operators, Proc. Amer. Math. Soc. 4 (1953), 723–728. MR 59483, DOI 10.1090/S0002-9939-1953-0059483-2
- John Bunce, Characters on singly generated $C^{\ast }$-algebras, Proc. Amer. Math. Soc. 25 (1970), 297–303. MR 259622, DOI 10.1090/S0002-9939-1970-0259622-4
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. MR 203464, DOI 10.1090/S0002-9939-1966-0203464-1 Paul R. Halmos, Introduction to Hilbert space, Chelsea, New York, 1957.
- Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 499-505
- MSC: Primary 47.30; Secondary 46.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283602-7
- MathSciNet review: 0283602