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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An index formula for $ n$-tuple of shifts on polydisk


Author: Ke Ren Yan
Journal: Proc. Amer. Math. Soc. 121 (1994), 747-754
MSC: Primary 47A13; Secondary 47A53, 47B20
DOI: https://doi.org/10.1090/S0002-9939-1994-1185275-3
MathSciNet review: 1185275
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Abstract: Let $ ({M_{{z_1}}}, \ldots ,{M_{{z_n}}})$ be an n-tuple of shift operators on the polydisk $ {l^2}({{\mathbf{Z}}^n})$; we compress it to a variety of subspaces of $ {l^2}({{\mathbf{Z}}^n})$ that are combinatorially constructed. The main result is a multivariate Fredholm index formula, which links the indices of the n-tuples to their combinatorial data in the definitions of the subspaces.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1185275-3
Article copyright: © Copyright 1994 American Mathematical Society