ON SYMMETRY OF THE (STRONG) BIRKHOFF-JAMES ORTHOGONALITY IN HILBERT C*-MODULES

被引：19

作者：

Arambasic, Ljiljana ^{[1
]}

Rajic, Rajna ^{[2
]}

机构：

[1] Univ Zagreb, Dept Math, Zagreb 41000, Croatia

[2] Univ Zagreb, Fac Min Geol & Petr Engn, Zagreb 41000, Croatia

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2016年 / 7卷 / 01期

关键词：

Hilbert C*-modules; inner product orthogonality; Birkhoff-James orthogonality; strong Birkhoff-James orthogonality; symmetry; MAPS;

D O I：

10.1215/20088752-3158195

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we prove that the Birkhoff-James orthogonality, as well as the strong Birkhoff-James orthogonality, is a symmetric relation in a full Hilbert A-module V if and only if at least one of the underlying C*-algebras A or K(V) is isomorphic to C.

引用

页码：17 / 23

页数：7

共 10 条

[1] On three concepts of orthogonality in Hilbert C*-modules
Arambasic, Lj.
Rajic, R.
[J]. LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (07) : 1485 - 1500
[2] A STRONG VERSION OF THE BIRKHOFF-JAMES ORTHOGONALITY IN HILBERT C*-MODULES
Arambasic, Ljiljana
Rajic, Rajna
[J]. ANNALS OF FUNCTIONAL ANALYSIS, 2014, 5 (01): : 109 - 120
[3] The Birkhoff-James orthogonality in Hilbert C*-modules
Arambasic, Ljiljana
Rajic, Rajna
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (07) : 1913 - 1929
[4] Characterization of Birkhoff-James orthogonality
Bhattacharyya, Tirthankar
Grover, Priyanka
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 407 (02) : 350 - 358
[5] Birkhoff G., 1935, Duke Math. J., V1, P169, DOI DOI 10.1215/S0012-7094-35-00115-6.H17I
[6] On maps that preserve orthogonality in normed spaces
Blanco, A.
Turnsek, A.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2006, 136 : 709 - 716
[7] JAMES RC, 1947, T AM MATH SOC, V61, P265
[8] LANCE C, 1995, LONDON MATH SOC LECT, V210
[9] Orthogonality and disjointness preserving linear maps between Fourier and Fourier-Stieltjes algebras of locally compact groups
Lau, Anthony To-Ming
Wong, Ngai-Ching
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (04) : 562 - 593
[10] Wegge-Olsen N.E., 1993, K THEORY C ALGEBRAS

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