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 $<T(x),T(y)>=|\lambda {|}^2<x,y>$ 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.

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

References in corpus (2)

• Adjointability of densely defined closed operators and the Magajna-Schweizer Theorem
• Generalized inverses and polar decomposition of unbounded regular operators on Hilbert $C^{\ast }$-modules

Cited by in corpus (4)

• Angle Preserving Mappings
• Linear orthogonality preservers of Hilbert $C^{\ast }$-modules over general $C^{\ast }$-algebras
• Linear orthogonality preservers of Hilbert $C^{\ast }$-modules over $C^{\ast }$-algebras with real rank zero
• B-spline interpolation problem in Hilbert C*-modules