Complemented subspaces isomorphic to \(\ell_ p\) in tensor products and operator spaces (Q1204775)

The principal results obtained in the paper are the following: 1. Suppose that \(1\leq q<p\leq r\leq \infty\). If a Banach space \(X\) has no complemented subspaces isomorphic to \(\ell_ q\), then \(X\otimes_{\varepsilon_ r}\ell_ p\) does not contain complemented subspaces isomorphic to \(\ell_ q\). 2. Suppose that \(1\leq r\leq p<q\leq\infty\). If a Banach space \(X\) has no complemented subspaces isomorphic to \(\ell_ q\), then \(\ell_ p\otimes_{g_ r}X\) does not contain complemented subspaces isomorphic to \(\ell_ q\).