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Activities

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Beginning 2009-11-09 00:00:00 2009-11-09 00:00:00 Linear orthogonality preservers of Hilbert C*-modules Prof. Ngai-Ching Wong,National Sun Yat-sen University) 3rd General Building R734 Click here to read Let \$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. 2009-11-05 17:15:20