From: "G. A. Edgar" <edgar@math.ohio-state.edu>
Subject: Re: Projections in Banach space
Date: Sat, 20 Jan 2001 17:13:07 -0500
Newsgroups: sci.math
Summary: Banach spaces with projections to all closed subspaces are Hilbert spaces

In article <3A69F4C0.F942B8CC@comtv.ru>, qq [Innocenti Maresin]
<av95@comtv.ru> wrote:

> If V is a Hilbert space then it has the property that if H is any
> closed subspace then there is a bounded projection from V onto H.
>
> If X is a Banach space with this property then must X be isomorphic to
> a Hilbert space ?

Yes, if "isomorphic" means linearly homeomorphic, as usual in
Banach space theory.

It's probably in Lindenstraus & Tzafriri, CLASSICAL BANACH SPACES.

-- 
Gerald A. Edgar              edgar@math.ohio-state.edu