Proportional Subspaces of Spaces with Unconditional Basis Have Good Volume Properties
Proportional Subspaces of Spaces with Unconditional Basis Have Good Volume Properties
A generalization of Lozanovskii's result is proved. Let E be k-dimensional sub-space of an n-dimensional Banach space with unconditional basis. Then there exist x 1,…, x k ⊂ E such that B E ⊂ absconv{x 1,…, x k } and $$ {\left( {\frac{{vol\left( {absconv\left\{ {{x_1}, \ldots {x_k}} \right\}} \right)}} {{vol\left( …