Orthogonality preserving linear maps on group algebras

Abstract

AbstractWe consider several types of orthogonality conditions on the group algebra L1(G) of a locally compact group G such as f$\ast $g = 0, f$\ast $g☆ = 0, f☆$\ast $g = 0, f$\ast $g = g$\ast $f = 0 and f$\ast $g☆ = g☆$\ast $f = 0, and we describe the linear maps Φ: L1(G) → L1(H) between the group algebras of locally compact groups G and H that take orthogonal functions of L1(G) into orthogonal functions of L1(H). Roughly speaking, they are weighted homomorphisms in the case where we are concerned with the one-sided orthogonality conditions and weighted Jordan homomorphisms in the case where we treat the two-sided orthogonality conditions.