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Invariant Subspaces on ${{\mathbb{T}}^{N}}$ and ${{\mathbb{R}}^{N}}$

Published online by Cambridge University Press:  20 November 2018

Michio Seto
Michio Seto*
Affiliation:
Mathematical Institute Tohoku University Sendai 980-8578 Japan, email: [email protected]
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Abstract

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Let $N$ be an integer which is larger than one. In this paper we study invariant subspaces of ${{L}^{2}}({{\mathbb{T}}^{N}})$ under the double commuting condition. A main result is an $N$-dimensional version of the theorem proved by Mandrekar and Nakazi. As an application of this result, we have an $N$-dimensional version of Lax's theorem.

Keywords

47A1547B47invariant subspaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 1 , 01 March 2004 , pp. 100 - 107
Copyright
Copyright © Canadian Mathematical Society 2004

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