Exotic indecomposable systems of four subspaces in a Hilbert space

Masatoshi Enomoto; Yasuo Watatani

doi:10.1007/s00020-007-1512-2

Exotic indecomposable systems of four subspaces in a Hilbert space

Masatoshi Enomoto, Yasuo Watatani

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We study the relative position of four (closed) subspaces in a Hilbert space. For any positive integer n, we give an example of exotic indecomposable system S 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 using certain nice sequences construced by Jiang and Wang in their study of strongly irreducible operators.

Original language	English
Pages (from-to)	149-164
Number of pages	16
Journal	Integral Equations and Operator Theory
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/s00020-007-1512-2
Publication status	Published - Oct 2007

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory

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abstract = "We study the relative position of four (closed) subspaces in a Hilbert space. For any positive integer n, we give an example of exotic indecomposable system S 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 using certain nice sequences construced by Jiang and Wang in their study of strongly irreducible operators.",

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AB - We study the relative position of four (closed) subspaces in a Hilbert space. For any positive integer n, we give an example of exotic indecomposable system S 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 using certain nice sequences construced by Jiang and Wang in their study of strongly irreducible operators.

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