Linear rank and corank preserving maps on B(H) and an application to *-semigroup isomorphisms of operator ideals

摘要

We characterize linear rank-k nonincreasing, rank-k preserving, and corank-k preserving maps on B(H), the algebra of all bounded linear operators on the Hilbert space H. This unifies and extends finite-dimensional results and results on linear rank-l nonincreasing and rank-l preserving maps in the infinite-dimensional case. We conclude with an application to *-semigroup isomorphisms of operator ideals. (C) 1998 Elsevier Science Inc. All rights reserved. [References: 20]