Toeplitz algebras, subnormal tuples and rigidity on reproducing C[z1,…,zd]-modules |
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Authors: | Kunyu Guo Junyun Hu |
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Affiliation: | a Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China b Institute of Mathematics, Jiaxing University, Jiaxing 340001, People's Republic of China |
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Abstract: | This paper mainly considers Toeplitz algebras, subnormal tuples and rigidity concerning reproducing C[z1,…,zd]-modules. By making use of Arveson's boundary representation theory, we find there is more rigidity in several variables than there is in single variable. We specialize our attention to reproducing C[z1,…,zd]-modules with -invariant kernels by examining the spectrum and the essential spectrum of the d-tuple {Mz1,…,Mzd}, and deducing an exact sequence of C∗-algebras associated with Toeplitz algebra. Finally, we deal with Toeplitz algebras defined on Arveson submodules and rigidity of Arveson submodules. |
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Keywords: | 47A13 47A20 46H25 46C99 |
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