Beginning2009-11-09 00:00:00
Ending2009-11-09 00:00:00
Event titleLinear orthogonality preservers of Hilbert C*-modules
SpeakerProf. Ngai-Ching Wong,National Sun Yat-sen University)
Place3rd General Building R734
DescriptionClick here to read
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NoteLet $A$ be a C*-algebra. A Banach space $X$ is called a Hilbert $A$-module if $X$ is a left $A$-module, and there is an $A$-valued inner product defined on $X$ such that $\|x\|^2 = \|\|$. When $A$ is the complex numbers, Hilbert $\mathbb{C}$-modules are simply Hilbert spaces. It is know that the norm, the inner product and the orthogonality structures of a Hilbert space determine each other. Recently, we (Leung, Ng and Wong) successfully extended these equivalences to general Hilbert C*-modules. This in particular includes the case of Hilbert bundles, in which $A$ is an abelian C*-algebra. More precisely, two Hilbert bundles are unitarily isomorphic if and only if there is a bijective linear map between them preserving the orthogonality of continuous vector sections. We also get a complete solution for the non-abelian case, although it might be too technical to be covered in this hourly talk.
Last Update Time2009-11-05 17:15:20
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