On two long standing open problems on Lp-spaces

Authors

  • M.M. Popov Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine, Pomeranian University in Słupsk, 76-200, Słupsk, Poland https://orcid.org/0000-0002-3165-5822
https://doi.org/10.15330/cmp.12.1.229-241

Keywords:

Lp-spaces, complemented subspace, unconditional basis
Published online: 2020-06-29

Abstract

The present note was written during the preparation of the talk at the International Conference dedicated to 70-th anniversary of Professor O. Lopushansky, September 16-19, 2019, Ivano-Frankivsk (Ukraine). We focus on two long standing open problems. The first one, due to Lindenstrauss and Rosenthal (1969), asks of whether every complemented infinite dimensional subspace of L1 is isomorphic to either L1 or 1. The second problem was posed by Enflo and Rosenthal in 1973: does there exist a nonseparable space Lp(μ) with finite atomless μ and 1<p<, p2, having an unconditional basis? We analyze partial results and discuss on some natural ideas to solve these problems.

How to Cite
(1)
Popov, M. On Two Long Standing Open Problems on Lp-Spaces. Carpathian Math. Publ. 2020, 12, 229-241.