A constructive approach to minimal projections in Banach spaces |
| |
Authors: | David L. Motte |
| |
Affiliation: | Department of Mathematics, Auburn University, Auburn, Alabama 36849, U.S.A. |
| |
Abstract: | Let X be a Banach space and Y a finite-dimensional subspace of X. Let P be a minimal projection of X onto Y. It is shown (Theorem 1.1) that under certain conditions there exist sequences of finite-dimensional “approximating subspaces” Xm and Ym of X with corresponding minimal projections Pm: Xm → Ym, such that limm→∞ Pm = P. Moreover, a certain related sequence of projections im○Pm○πm: X → Y has cluster points in the strong operator topology, each of which is a minimal projection of X onto Y. When X = C[a, b] the result reduces to a theorem of [7.]. It is shown (Corollary 1.11) that the hypothesis of Theorem 1.1 holds in many important Banach spaces, including C[a, b], LP[a, b] and lP for 1 p < ∞, and c0, the space of sequences converging to zero in the sup norm. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|