Ghosh, P and Sain, D and Paul, K
(2017)
*On symmetry of Birkhoff-James orthogonality of linear operators.*
In: Advances in Operator Theory, 2
(4).
pp. 428-434.

## Abstract

A bounded linear operator T on a normed linear space X is said to be right symmetric (left symmetric) if A ⊥B T ⇒ T ⊥B A (T⊥B A ⇒ A ⊥B T) for all A ∈ B(X), the space of all bounded linear operators on X. Turnšek [Linear Algebra Appl., 407 (2005), 189-195] proved that if X is a Hilbert space then T is right symmetric if and only if T is a scalar multiple of an isometry or coisometry. This result fails in general if the Hilbert space is replaced by a Banach space. The characterization of right and left symmetric operators on a Banach space is still open. In this paper we study the orthogonality in the sense of Birkhoff-James of bounded linear operators on (ℝn,. ∞) and characterize the right symmetric and left symmetric operators on (ℝn, .∞).

Item Type: | Journal Article |
---|---|

Publication: | Advances in Operator Theory |

Publisher: | Tusi Mathematical Research Group (TMRG) |

Additional Information: | The copyright for this article belongs to the Tusi Mathematical Research Group (TMRG). |

Keywords: | Birkhoff-James Orthogonality; Left syemmetric operator; Right symmetric operator |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 17 Jul 2022 05:43 |

Last Modified: | 17 Jul 2022 05:43 |

URI: | https://eprints.iisc.ac.in/id/eprint/74485 |

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