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A generalization of the Roberts orthogonality: from normed linear spaces to C∗ -algebras

Faryad, E and Khurana, D and Moslehian, MS and Sain, D (2022) A generalization of the Roberts orthogonality: from normed linear spaces to C∗ -algebras. In: Monatshefte fur Mathematik .

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Official URL: https://doi.org/10.1007/s00605-022-01799-7


We introduce and study an extension of the Roberts orthogonality, in the setting of C∗-algebras. More precisely, in a C∗-algebra A, for a, b∈ A and a nonempty subset of A, say B, a is called B-Roberts orthogonal to b, denoted by a⊥RBb, if ‖ a+ bc‖ = ‖ a- bc‖ for all c∈ B. For certain special C∗-algebras, including the C∗-algebra of all 2 × 2 complex matrices, we obtain a nontrivial subset B such that the B-Roberts orthogonality coincides with the usual orthogonality. We also introduce a new concept of smoothness in normed linear spaces in terms of the additivity property of the usual Roberts orthogonality. A complete characterization of the same is obtained in the case of the classical ℓ∞n spaces.

Item Type: Journal Article
Publication: Monatshefte fur Mathematik
Publisher: Springer
Additional Information: The copyright for this article belongs to Springer.
Keywords: Additivity; C∗-algebra; Inner product orthogonality; Roberts orthogonality
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 05 Jan 2023 06:55
Last Modified: 05 Jan 2023 06:55
URI: https://eprints.iisc.ac.in/id/eprint/78743

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