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

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

2009-07-17

arxiv.org/abs/0907.2983v3

Mathematics

Operator Algebras

13 pages / Thm. 1.3, second paragraph of proof - corrected, minor changes of formulations in the text, references updated

Scientific paper

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 \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 fulfils the equality $ = | \lambda |^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.

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