Orthogonality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules

Abstract

We investigate orthonormality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules to obtain their general structure. Orthogonality-preserving bounded module maps T act as a multiplication by an element λof the center of the multiplier algebra of the C*-algebra of coefficients combined with an isometric module operator as long as some polar decomposition conditions for the specific element λare fulfilled inside that multiplier algebra. Generally, T always fulfils the equality $ = | λ|^2 < x,y>$ for any elements x,y of the Hilbert C*-module. At the contrary, C*-conformal and conformal bounded C*-linear mappings are shown to be only the positive real multiples of isometric module operators.