Von Neumann's theorem for linear relations

被引：10
|
作者：
Sandovici, Adrian [1 ]
机构：
[1] Gheorghe Asachi Tech Univ Iasi, Dept Math & Informat, Iasi, Romania
来源：
LINEAR & MULTILINEAR ALGEBRA | 2018年 / 66卷 / 09期
关键词：
Hilbert space; closed linear relation; nonnegative linear relation; selfadjoint linear relation; von Neumann theorem; ADJOINT; EXTENSIONS; OPERATORS; SUMS;
D O I：
10.1080/03081087.2017.1369930
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Assume that T is a linear relation acting between two real or complex Hilbert spaces H and K, respectively. T is shown to be closed if and only if the linear relations T * T and TT * are both selfadjoint linear relations on the corresponding Hilbert spaces H and K, respectively.
引用
收藏
页码：1750 / 1756
页数：7
相关论文
共 50 条
  • [31] GEODESICS OF PROJECTIONS IN VON NEUMANN ALGEBRAS
    Andruchow, Esteban
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (10) : 4501 - 4513
  • [32] Projections and Traces on von Neumann Algebras
    Bikchentaev, A. M.
    Abed, S. A.
    LOBACHEVSKII JOURNAL OF MATHEMATICS, 2019, 40 (09) : 1260 - 1267
  • [33] ON VON NEUMANN-JORDAN CONSTANTS
    Hashimoto, Kazuo
    Nakamura, Gen
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 87 (03) : 371 - 375
  • [34] Projections and Traces on von Neumann Algebras
    A. M. Bikchentaev
    S. A. Abed
    Lobachevskii Journal of Mathematics, 2019, 40 : 1260 - 1267
  • [35] An Index Theorem for Linear Relations and Its Applications to the Study of Block Relation Matrices
    Ghorbel, Ayoub
    Mnif, Maher
    FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2023, 57 (SUPPL 1) : 1 - 16
  • [36] Star Order and Topologies on von Neumann Algebras
    Bohata, Martin
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (04)
  • [37] Regular semigroups of endomorphisms of von Neumann factors
    Amosov, GG
    Bulinskii, AV
    Shirokov, ME
    MATHEMATICAL NOTES, 2001, 70 (5-6) : 583 - 598
  • [38] On Classification of von Neumann Algebras in a Space with Conjugation
    Vladova, E. V.
    Matveichuk, M. S.
    Ogai, Yu. G.
    RUSSIAN MATHEMATICS, 2014, 58 (04) : 1 - 6
  • [39] DERIVATIONS OF MURRAY-VON NEUMANN ALGEBRAS
    Kadison, Richard V.
    Liu, Zhe
    MATHEMATICA SCANDINAVICA, 2014, 115 (02) : 206 - 228
  • [40] Regular Semigroups of Endomorphisms of von Neumann Factors
    G. G. Amosov
    A. V. Bulinskii
    M. E. Shirokov
    Mathematical Notes, 2001, 70 : 583 - 598
12345