Relative position of three subspaces in a Hilbert space

2014/07/25 by Masatoshi Enomoto, Enomoto, Masatoshi, Yasuo Watatani +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory #math.FA #math.OA #msc:15A21 #msc:16G20 #msc:16G60 #msc:46C67 #msc:47A15

paper · pdf · doi:10.48550/arxiv.1407.6852

22 pages, Proposition 4.1 added, typos added, references added. arXiv admin note: substantial text overlap with arXiv:math/0404545

arxiv created 2014/10/14 · arxiv updated 2014/10/15

Abstract

We study the relative position of three subspaces in a separable infinite-dimensional Hilbert space. In the finite-dimensional case, Brenner described the general position of three subspaces completely. We extend it to a certain class of three subspaces in an infinite-dimensional Hilbert space. We also give a partial result which gives a condition on a system to have a (dense) decomposition containing a pentagon.

Citations

• Relative position of four subspaces in a Hilbert space

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