Orthogonality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2009
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915259884765184 |
|---|---|
| author | Frank, Michael Mishchenko, Alexander S. Pavlov, Alexander A. |
| author_facet | Frank, Michael Mishchenko, Alexander S. Pavlov, Alexander A. |
| contents | 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 $<T(x),T(y) > = | λ|^2 < x,y>$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0907_2983 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | Orthogonality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules Frank, Michael Mishchenko, Alexander S. Pavlov, Alexander A. Operator Algebras Functional Analysis 46L08, 42C15, 42C40 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 $<T(x),T(y) > = | λ|^2 < x,y>$ 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. |
| title | Orthogonality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules |
| topic | Operator Algebras Functional Analysis 46L08, 42C15, 42C40 |
| url | https://arxiv.org/abs/0907.2983 |