Uniform convexity and uniform smoothness of ℓᵖ(Ĝ) spaces based on the Hilbert-Schmidt ideal.
DOI:
https://doi.org/10.70474/kmj-2024-1-01Keywords:
Compact group, uniformly smooth Banach space, uniformly convex Banach space, ℓᵖ -spaces associated with a compact groupsAbstract
In this paper, we study uniform convexity and uniform smoothness properties of ℓᵖ-spaces associated with the unitary dual of a compact group based on the Hilbert-Schmidt ideal.
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Akhymbek, M., Ruzhansky, M., Tulenov, K. On geometric properties of $ell^{p} $-spaces on unitary duals of compact groups, arXiv preprint, arXiv:2404.08337, 2024.
Clarkson J.A. Uniformly convex spaces, Transactions of the American Mathematical Society, 40, 3, 1936, 396–414. DOI: https://doi.org/10.2307/1989630
Day M.M. Uniform convexity in factor and conjugate spaces, Annals of Mathematics, 45, 2, 1944, 375–385. DOI: https://doi.org/10.2307/1969275
Diestel J. Geometry of Banach spaces-selected topics, Springer, 485, 2006.
Edwards R.E. Integration and harmonic analysis on compact groups, Cambridge University Press, 10, 1972.
Fischer V., Ruzhansky M. Quantization on nilpotent Lie groups, Springer Nature, 2016.
Gohberg I., Krein M.G. Introduction to the theory of linear non-selfadjoint operators, American Mathematical Soc., No. 18, 1978.
Hewitt E., Ross K.A. Abstract Harmonic Analysis. Vol. II: Structure and Analysis for Compact Groups. Analysis on Locally Compact Abelian Groups, 2nd Printing edn., Grundlehren der Mathematischen Wissenschaften, 152, 1994.
Lindenstrauss J. On the modulus of smoothness and divergent series in Banach spaces, Michigan Mathematical Journal, 10, 3, 1963, 241–252. DOI: https://doi.org/10.1307/mmj/1028998906
Lindenstrauss J., Tzafriri L. Classical Banach spaces II: function spaces, Springer Science and Business Media, 97, 2013.
Ruzhansky, M., Turunen V. Pseudo-differential operators and symmetries: background analysis and advanced topics. Vol. 2, Springer Science and Business Media, 2009.
Simon, B. Trace ideals and their applications, American Mathematical Soc., No. 120, 2005.
Tulenov K.S., Akhymbek M.E., Kassymov A.A. Clarkson inequalities on Lp(G) space associated with compact Lie group, Journal of Pseudo-Differential Operators and Applications, 9, 2018, 443–450. DOI: https://doi.org/10.1007/s11868-017-0187-y
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