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Sibirsk. Mat. Zh., 2017, Volume 58, Number 6, Pages 1228–1235 (Mi smj2933)  

On subspaces of Cesàro spaces

S. V. Astashkin

Samara National Research University, Samara, Russia

Abstract: We obtain a characterization of subspaces of $L_p$, with $1<p<\infty$, on which the $L_p$-norm is equivalent to the norm of the Cesàro space $\operatorname{Ces}_p$. Also, we show that $\operatorname{Ces}_p$ has a complemented copy of the Cesàro sequence space $\operatorname{ces}_p$.

Keywords: $L_p$-space, Cesàro space, $\Lambda(p)$-space, isomorphism.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.470.2016/1.4
Russian Foundation for Basic Research 17-01-00138
The author was supported by the Ministry of Education and Science in the framework of a State Task (Grant 1.470.2016/1.4) and partially supported by the Russian Foundation for Basic Research (Grant 17-01-00138).


DOI: https://doi.org/10.17377/smzh.2017.58.604

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English version:
Siberian Mathematical Journal, 2017, 58:6, 952–958

Bibliographic databases:

UDC: 517.982.27
Received: 02.03.2017

Citation: S. V. Astashkin, “On subspaces of Cesàro spaces”, Sibirsk. Mat. Zh., 58:6 (2017), 1228–1235; Siberian Math. J., 58:6 (2017), 952–958

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\paper On subspaces of Ces\`aro spaces
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