Spectral permanence for joint spectra

Raul E. Curto

doi:10.1090/S0002-9947-1982-0645336-8

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Spectral permanence for joint spectra

Raul E. Curto

Transactions of the American Mathematical Society, Vol.270(2), pp.659-665

1982

DOI: 10.1090/S0002-9947-1982-0645336-8

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Abstract

For a C*-subalgebra A of a C*-algebra B and a commuting n-tuple a = (a,,... ,a„) of elements of A, we prove that Sp(a, A) = Sp(a, B), where Sp denotes Taylor spectrum. As a consequence we prove that 0 g Sp(a, A) if and only if (FORMULA PRESENT) is invertible, where d{ is the i th boundary map in the Koszul complex for A. More generally, we show that os k(a, A) = os k(a, B) and o„ k(a, A) = a„ k(a, B) (all k), where os . and oa„ . are the joint spectra considered by Z. Slodkowski.

Joint spectra

Spectral permanence

Universal representation

Von Neumann algebras

Details

Title: Subtitle: Spectral permanence for joint spectra
Creators: Raul E. Curto - University of Iowa, Mathematics
Resource Type: Journal article
Publication Details: Transactions of the American Mathematical Society, Vol.270(2), pp.659-665
DOI: 10.1090/S0002-9947-1982-0645336-8
ISSN: 0002-9947
eISSN: 1088-6850
Number of pages: 7
Language: English
Date published: 1982
Academic Unit: Mathematics
Record Identifier: 9984240867002771

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