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1. CMB 2008 (vol 51 pp. 604)
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The Invariant Subspace Problem for Non-Archimedean Banach Spaces It is proved that every infinite-dimensional
non-archimedean Banach space of countable type admits a linear
continuous operator without a non-trivial closed invariant
subspace. This solves a problem stated by A.~C.~M. van Rooij and
W.~H. Schikhof in 1992.
Keywords:invariant subspaces, non-archimedean Banach spaces Categories:47S10, 46S10, 47A15 |
2. CMB 2004 (vol 47 pp. 100)
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Invariant Subspaces on $\mathbb{T}^N$ and $\mathbb{R}^N$ 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 Categories:47A15, 47B47 |