On the Unital C*-Algebras Generated by Certain Subnormal Tuples

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On the Unital C*-Algebras Generated by Certain Subnormal Tuples

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Title: On the Unital C*-Algebras Generated by Certain Subnormal Tuples
Author: ATHAVALE, A
Abstract: We consider an important class of subnormal operator m-tuples M(p) (p = m, m+ 1, ...) that is associated with a class of reproducing kernel Hilbert spaces H(p) (with M(m) being the multiplication tuple on the Hardy space of the open unit ball B(2m) in C(m) and M(m+1) being the multiplication tuple on the Bergman space of B(2m)). Given any two C*-algebras A and B from the collection {C*(M(p)), C*((M) over tilde (p)) : p >= m}, where C*(M(p)) is the unital C*-algebra generated by M(p) and C*((M) over tilde (p)) the unital C*-algebra generated by the dual (M) over tilde (p) of M(p), we verify that A and B are either *-isomorphic or that there is no homotopy equivalence between A and B. For example, while C*(M(m)) and C*(M(m+1)) are well-known to be *-isomorphic, we find that C*((M) over tilde (m)) and C*((M) over tilde (m+1)) are not even homotopy equivalent; on the other hand, C*(M(m)) and C*((M) over tilde (m)) are indeed *-isomorphic. Our arguments rely on the BDF-theory and K-theory.
URI: http://dx.doi.org/10.1007/s00020-010-1815-6
http://dspace.library.iitb.ac.in/xmlui/handle/10054/5136
http://hdl.handle.net/10054/5136
Date: 2010


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