Department of Mathematics, University of Maribor, PEF, Koroška 160, SI-2000 Maribor, Slovenia
Abstract:
Let A be a triangular algebra. The problem of describing the form of a bilinear map satisfying B(x,x)x=xB(x,x) for all xA is considered. As an application, commutativity preserving maps and Lie isomorphisms of certain triangular algebras (e.g., upper triangular matrix algebras and nest algebras) are determined.