Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras

A nonlinear map phi between operator algebras is said to be a numerical radius isometry if w(phi(T-S))=w(T-S) for all T, S in its domain algebra, where w(T) stands for the numerical radius of T. Let N and M be two atomic nests on complex Hilbert spaces H and K, respectively. Denote Alg N the nest algebra associated with N and D-N=Alg N boolean AND(Alg N)* the diagonal algebra. We give a thorough classification of weakly continuous numerical radius isometrics from Alg N onto Alg M and a thorough classification of numerical radius isometries from D-N onto D-M. (C) 2003 Elsevier Inc. All rights reserved.