Further generalized refinement of Young’s inequalities for τ -mesurable operators

In this paper, we prove that if , > 0 and 0 ≤ ≤ 1. Then for all positive integer (1) - For ∈ , we have (2) - For ∈ , we have we also prove two similar inequalities for the cases ∈ and ∈ . These inequalities provides a generalization of an important refinements of the Young inequality obtained in...

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Bibliographic Details
Published in:Moroccan journal of pure and applied analysis 2021-07, Vol.7 (2), p.214-226
Main Authors: Ighachane, Mohamed Amine, Akkouchi, Mohamed
Format: Article
Language:English
Subjects:
26D07
47A63
AM-GM inequality
Determinants
norms
p-norms
Trace
Young’s inequality
τ-mesurable operators
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Summary:In this paper, we prove that if , > 0 and 0 ≤ ≤ 1. Then for all positive integer (1) - For ∈ , we have (2) - For ∈ , we have we also prove two similar inequalities for the cases ∈ and ∈ . These inequalities provides a generalization of an important refinements of the Young inequality obtained in 2017 by S. Furuichi. As applications we shall give some refined Young type inequalities for the traces, determinants, and -norms of positive τ-measurable operators.
ISSN:2351-8227
2351-8227
DOI:10.2478/mjpaa-2021-0015