English

Relative position of three subspaces in a Hilbert space

Operator Algebras 2014-10-15 v2 Functional Analysis

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.

Keywords

Cite

@article{arxiv.1407.6852,
  title  = {Relative position of three subspaces in a Hilbert space},
  author = {Masatoshi Enomoto and Yasuo Watatani},
  journal= {arXiv preprint arXiv:1407.6852},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-22T05:13:06.507Z