Segments of bounded linear idempotents on a Hilbert space

摘要

Let H be a separable Hilbert space. We prove that any two homotopic idempotents in the algebra C(H) may be connected by a piecewise affine idempotent-valued path consisting of 4 segments at most. Moreover, we show that this constant is optimal provided H has infinite dimension. We also explain how this result is linked to the problem of finding common complements for two closed subspaces of H. (c) 2005 Elsevier Inc. All rights reserved.