@article{Popov_2020, title={On two long standing open problems on $L_p$-spaces}, volume={12}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/3907}, DOI={10.15330/cmp.12.1.229-241}, abstractNote={<p>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.</p>}, number={1}, journal={Carpathian Mathematical Publications}, author={Popov, M.M.}, year={2020}, month={Jun.}, pages={229-241} }