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Invariant Subspaces on $\mathbb{T}^N$ and $\mathbb{R}^N$ |
Canad. Math. Bull. 47(2004), 100-107
Published:2004-03-01
Printed: Mar 2004
Printed: Mar 2004
- Michio Seto
Abstract
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: | invariant subspaces |
| MSC Classifications: |
47A15 - Invariant subspaces [See also 47A46] 47B47 - Commutators, derivations, elementary operators, etc. |