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

We investigate orthonormality-preserving, C*-conformal and conformal module mappings on full Hilbert C*-modules to obtain their general structure. Orthogonality-preserving bounded module maps T act as a multiplication by an element lambda of 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 lambda are fulfilled inside that multiplier algebra. Generally, T always fulfills the equality < T(x), T(y)> = vertical bar lambda vertical bar(2) < x, y > for any elements x, y of the Hilbert C*-module. At the contrary, C*-conformal and conformal bounded module maps are shown to be only the positive real multiples of isometric module operators. (C) 2010 Elsevier Inc. All rights reserved.