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January 2019 Continuous generalization of Clarkson–McCarthy inequalities
Dragoljub J. Kečkić
Banach J. Math. Anal. 13(1): 26-46 (January 2019). DOI: 10.1215/17358787-2018-0014

Abstract

Let G be a compact Abelian group, let μ be the corresponding Haar measure, and let Gˆ be the Pontryagin dual of G. Furthermore, let Cp denote the Schatten class of operators on some separable infinite-dimensional Hilbert space, and let Lp(G;Cp) denote the corresponding Bochner space. If GθAθ is the mapping belonging to Lp(G;Cp), then kGˆGk(θ)¯AθdθppGAθppdθ,p2, kGˆGk(θ)¯Aθdθpp(GAθpqdθ)p/q,p2, kGˆGk(θ)¯Aθdθpq(GAθppdθ)q/p,p2. If G is a finite group, then the previous equations comprise several generalizations of Clarkson–McCarthy inequalities obtained earlier (e.g., G=Zn or G=Z2n), as well as the original inequalities, for G=Z2. We also obtain other related inequalities.

Citation

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Dragoljub J. Kečkić. "Continuous generalization of Clarkson–McCarthy inequalities." Banach J. Math. Anal. 13 (1) 26 - 46, January 2019. https://doi.org/10.1215/17358787-2018-0014

Information

Received: 17 January 2018; Accepted: 19 April 2018; Published: January 2019
First available in Project Euclid: 28 September 2018

zbMATH: 07002030
MathSciNet: MR3894063
Digital Object Identifier: 10.1215/17358787-2018-0014

Subjects:
Primary: 47A30
Secondary: 43A25, 47B10

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 1 • January 2019
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