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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 319, Pages 20–28
DOI: https://doi.org/10.4213/tm4250 (Mi tm4250) 		 
On Quasibases and Bases of Symmetric Spaces Consisting of Nonnegative Functions

S. V. Astashkina, P. A. Terekhinb

a Samara National Research University, Moskovskoye shosse 34, Samara, 443086 Russia
b Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia
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DOI: https://doi.org/10.4213/tm4250
Abstract: Based on the study of the geometric properties of unconditional quasibasic sequences, we show that in an arbitrary symmetric space there exists no unconditional quasibasis consisting of nonnegative functions. Moreover, we demonstrate that in an arbitrary Banach function lattice $X$ of type $p>1$ one can introduce an equivalent norm such that there exists no monotone (with respect to the new norm) basis in $X$ that consists of nonnegative functions.
Keywords: basis, quasibasis, basic sequence, symmetric space, Rademacher system, type of a Banach space.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-878
The work of the first author was supported within the development program of the Scientific and Educational Mathematical Center of the Volga Federal District (agreement no. 075-02-2022-878).
Received: October 17, 2021
Revised: November 25, 2021
Accepted: December 2, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 319, Pages 13–21
DOI: https://doi.org/10.1134/S0081543822050029
Bibliographic databases:
Document Type: Article
UDC: 517.982.27+517.518.3
Language: Russian
Citation: S. V. Astashkin, P. A. Terekhin, “On Quasibases and Bases of Symmetric Spaces Consisting of Nonnegative Functions”, Approximation Theory, Functional Analysis, and Applications, Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin, Trudy Mat. Inst. Steklova, 319, Steklov Math. Inst., Moscow, 2022, 20–28; Proc. Steklov Inst. Math., 319 (2022), 13–21
Citation in format AMSBIB
\Bibitem{AstTer22}
\by S.~V.~Astashkin, P.~A.~Terekhin
\paper On Quasibases and Bases of Symmetric Spaces Consisting of Nonnegative Functions
\inbook Approximation Theory, Functional Analysis, and Applications
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 319
\pages 20--28
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4250}
\crossref{https://doi.org/10.4213/tm4250}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 319
\pages 13--21
\crossref{https://doi.org/10.1134/S0081543822050029}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85148419992}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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