TY - JOUR
AU - Popov, M.M.
PY - 2020/06/29
Y2 - 2020/09/28
TI - On two long standing open problems on $L_p$-spaces
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 12
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.12.1.229-241
UR - https://scijournals.pnu.edu.ua/index.php/cmp/article/view/3907
SP - 229-241
AB - 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 $1<p<\infty$, $p
eq 2$, having an unconditional basis? We analyze partial results and discuss on some natural ideas to solve these problems.
ER -