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| TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES |
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Citation： |
CAO Guangfu.TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES[J].Chinese Annals of Mathematics B,2002,23(3):385~396 |
| Page view： 1353
Net amount： 847 |
Authors： |
CAO Guangfu; |
Foundation： |
Project supported by the National Natural Science Foundation of China. |
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| Abstract： |
The automorphism group of the Toeplitz $C^{*}$- algebra, ${\Cal J}(C^{1})$, generated by Toeplitz operators with $C^{1}$-symbols on Dirichlet space D is discussed; the $K_{0},K_{1}$-groups and the first cohomology group of ${\Cal J}(C^{1})$ are computed. In addition, the author proves that the spectra of Toeplitz operators with $C^{1}$-symbols are always connected, and discusses the algebraic properties of Toeplitz operators. In particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and $T_{\varphi }^{*}=T_{\bar{\varphi }}$ if and only if $T_{\varphi }$ is a scalar operator. |
Keywords： |
Dirichlet space, Toeplitz operator, Toeplitz algebra |
Classification： |
47B35 |
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