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Systems of two subspaces in a Hilbert space

Authors
  • Enomoto, Masatoshi1
  • Watatani, Yasuo2
  • 1 Koshien University, Takarazuka, Hyogo, 665-0006, Japan , Takarazuka (Japan)
  • 2 Kyushu University, Fukuoka, Japan , Fukuoka (Japan)
Type
Published Article
Journal
Advances in Operator Theory
Publisher
Springer International Publishing
Publication Date
Oct 07, 2020
Volume
6
Issue
1
Identifiers
DOI: 10.1007/s43036-020-00109-y
Source
Springer Nature
Keywords
License
Yellow

Abstract

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded operators are determined by unitarily equivalent classes of the operator ranges and the nullity of the original bounded operators giving graphs. We construct several non-isomorphic examples of two subspace systems in an infinite-dimensional Hilbert space. Even if we study n subspace systems for n≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \ge 3$$\end{document}, we can use the analysis of any two subspaces of the n subspaces.

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