Exotic indecomposable systems of four subspaces in a Hilbert space

Details Exotic indecomposable systems of four subspaces in a Hilbert space Exotic indecomposable systems of four subspaces in a Hilbert space

2006-07-04

arxiv.org/abs/math/0607085v1

Mathematics

Functional Analysis

16pages

Scientific paper

We study the relative position of four subspaces in a Hilbert space. For any positive integer n, we give an example of exotic indecomposable system of four subspaces in a Hilbert space whose defect is (2n+1)/3. By an exotic system, we mean a system which is not isomorphic to any closed operator system under any permutation of subspaces. We construct the examples by a help of certain nice sequences used by Jiang and Wang in their study of strongly irreducible operators.

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