Locally linearly dependent operators

Roy Meshulam and Peter Šemrl

Vol. 203 (2002), No. 2, 441–459

DOI: 10.2140/pjm.2002.203.441

Abstract

Let U and V be vector spaces over a field F. Linear operators T₁,…, T_n : U → V are locally linearly dependent if T₁u,…,T_nu are linearly dependent for every u ∈ U. We extend and unify known results on locally linearly dependent operators and present two applications of these new results, one in algebra and one in functional analysis.

Milestones

Received: 23 June 2000

Published: 1 April 2002