Translator Disclaimer
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 G ˆ be the Pontryagin dual of G . Furthermore, let C p denote the Schatten class of operators on some separable infinite-dimensional Hilbert space, and let L p ( G ; C p ) denote the corresponding Bochner space. If G θ A θ is the mapping belonging to L p ( G ; C p ) , then k G ˆ G k ( θ ) ¯ A θ d θ p p G A θ p p d θ , p 2 , k G ˆ G k ( θ ) ¯ A θ d θ p p ( G A θ p q d θ ) p / q , p 2 , k G ˆ G k ( θ ) ¯ A θ d θ p q ( G A θ p p d θ ) q / p , p 2 . If G is a finite group, then the previous equations comprise several generalizations of Clarkson–McCarthy inequalities obtained earlier (e.g., G = Z n or G = Z 2 n ), as well as the original inequalities, for G = Z 2 . We also obtain other related inequalities.

Citation

Download Citation

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

JOURNAL ARTICLE
21 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.13 • No. 1 • January 2019
Back to Top