Translator Disclaimer
June 2014 Banach envelopes of $p$-Banach lattices, $0<p<1$, and Cesàro spaces
Anna Kamińska, Pei-Kee Lin
Funct. Approx. Comment. Math. 50(2): 297-306 (June 2014). DOI: 10.7169/facm/2014.50.2.7

Abstract

In this note we characterize Banach envelopes of $p$-Banach lattices, $0<p<1$, such that their positive cones are $1$-concave. In particular we show that the Banach envelope of Cesàro sequence space $\widehat{ces_p(v)}$, $0<p<1$, coincides isometrically with the weighted $\ell_1(w)$ space where $w(n) = ||e_n||_{ces_p(v)}= (\sum_{i=n}^\infty i^{-p} v(i))^{1/p}$ and $e_n$ are the unit vectors. For Cesàro function space $Ces_p(v)$, $0<p<1$, its Banach envelope $\widehat{Ces_p(v)}$ is isometrically equal to $L_1(w)$ with $w(t) = (\int_t^\infty s^{-p} v(s) ds)^{1/p}$, $t\in (0,\infty)$.

Citation

Download Citation

Anna Kamińska. Pei-Kee Lin. "Banach envelopes of $p$-Banach lattices, $0<p<1$, and Cesàro spaces." Funct. Approx. Comment. Math. 50 (2) 297 - 306, June 2014. https://doi.org/10.7169/facm/2014.50.2.7

Information

Published: June 2014
First available in Project Euclid: 26 June 2014

zbMATH: 1312.46005
MathSciNet: MR3229063
Digital Object Identifier: 10.7169/facm/2014.50.2.7

Subjects:
Primary: 46A16
Secondary: 46A40, 46A45, 46B04, 46B42, 46B45

Rights: Copyright © 2014 Adam Mickiewicz University

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.50 • No. 2 • June 2014
Back to Top