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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The joint spectrum of commuting nonnormal operators

Author: John Bunce
Journal: Proc. Amer. Math. Soc. 29 (1971), 499-505
MSC: Primary 47.30; Secondary 46.00
MathSciNet review: 0283602
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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.

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Keywords: Joint spectrum, approximate spectrum, joint approximate spectrum, hyponormal operators
Article copyright: © Copyright 1971 American Mathematical Society