Annals of Functional Analysis

On symmetry of the (strong) Birkhoff–James orthogonality in Hilbert C-modules

Ljiljana Arambašić and Rajna Rajić

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 1 (2016), 17-23.

Dates
Received: 2 December 2014
Accepted: 16 February 2015
First available in Project Euclid: 15 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1444913695

Digital Object Identifier
doi:10.1215/20088752-3158195

Mathematical Reviews number (MathSciNet)
MR3449336

Zentralblatt MATH identifier
1352.46053

Subjects
Primary: 46L08: $C^*$-modules
Secondary: 46L05: General theory of $C^*$-algebras 46B20: Geometry and structure of normed linear spaces

Keywords
Hilbert $C^{*}$-modules inner product orthogonality Birkhoff–James orthogonality strong Birkhoff–James orthogonality symmetry

Citation

Arambašić, Ljiljana; Rajić, Rajna. On symmetry of the (strong) Birkhoff–James orthogonality in Hilbert $C^{*}$ -modules. Ann. Funct. Anal. 7 (2016), no. 1, 17--23. doi:10.1215/20088752-3158195. https://projecteuclid.org/euclid.afa/1444913695


Export citation

References

  • [1] L. Arambašić and R. Rajić, The Birkhoff–James orthogonality in Hilbert $C^{*}$-modules, Linear Algebra Appl. 437 (2012), no. 7, 1913–1929.
  • [2] L. Arambašić and R. Rajić, A strong version of the Birkhoff–James orthogonality in Hilbert $C^{*}$-modules, Ann. Funct. Anal. 5 (2014), no. 1, 109–120.
  • [3] L. Arambašić and R. Rajić, On three concepts of orthogonality in Hilbert $C^{*}$-modules, Linear Multilinear Algebra 63 (2015), no. 7, 1485–1500.
  • [4] T. Bhattacharyya and P. Grover, Characterization of Birkhoff–James orthogonality, J. Math. Anal. Appl. 407 (2013), no. 2, 350–358.
  • [5] G. Birkhoff, Orthogonality in linear metric spaces, Duke Math. J. 1 (1935), no. 2, 169–172.
  • [6] A. Blanco and A. Turnšek, On maps that preserve orthogonality in normed spaces, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), no. 4, 709–716.
  • [7] R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265–292.
  • [8] C. Lance, Hilbert $C^{*}$-Modules, London Math. Soc. Lecture Note Ser. 210, Cambridge Univ. Press, Cambridge, 1995.
  • [9] A. T.-M. Lau and N.-C. Wong, Orthogonality and disjointness preserving linear maps between Fourier and Fourier–Stieltjes algebras of locally compact groups, J. Funct. Anal. 265 (2013), no. 4, 562–593.
  • [10] N. E. Wegge-Olsen, $K$-Theory and $C^{*}$-Algebras, Oxford Univ. Press, Oxford, 1993.