On two long standing open problems on $L_p$-spaces | Zendy

M. M. Popov | Zendy

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On two long standing open problems on $L_p$-spaces

Author(s) -

M. M. Popov

Publication year - 2020

Publication title -

carpathian mathematical publications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.63

H-Index - 4

eISSN - 2313-0210

pISSN - 2075-9827

DOI - 10.15330/cmp.12.1.229-241

Subject(s) - subspace topology , mathematics , focus (optics) , space (punctuation) , combinatorics , pure mathematics , mathematical economics , mathematical analysis , philosophy , physics , linguistics , optics

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 $L_1$ is isomorphic to either $L_1$ or $\ell_1$. The second problem was posed by Enflo and Rosenthal in 1973: does there exist a nonseparable space $L_p(\mu)$ with finite atomless $\mu$ and $1

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