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Proceedings of the American Mathematical Society

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

 

 

Tensor products and the joint spectrum in Hilbert spaces


Authors: Zoia Ceauşescu and F.-H. Vasilescu
Journal: Proc. Amer. Math. Soc. 72 (1978), 505-508
MSC: Primary 47A10; Secondary 46M05
DOI: https://doi.org/10.1090/S0002-9939-1978-0509243-8
MathSciNet review: 509243
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Abstract: Given two complex Hilbert spaces X and Y and two commuting systems of linear continuous operators $ a = ({a_1}, \ldots ,{a_n})$ on X and $ b = ({b_1}, \ldots ,{b_m})$ on Y, the joint spectrum of the commuting system $ ({a_1} \otimes 1, \ldots ,{a_n} \otimes 1,1 \otimes {b_1}, \ldots ,1 \otimes {b_m})$ on $ X\bar \otimes Y$ is expressed by the Cartesian product of the joint spectrum of a with the joint spectrum of b.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0509243-8
Keywords: Tensor product, Hilbert space, joint spectrum
Article copyright: © Copyright 1978 American Mathematical Society