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 λ 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 λ are fulfilled inside that multiplier algebra. Generally, T always fulfills the equality 〈T(x),T(y)〉=2|λ|〈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.