Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras |
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| Authors: | Kenneth R. Davidson David R. Pitts |
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| Affiliation: | (1) Department of Pure Mathematics, University of Waterloo, N2L-3G1 Waterloo, ON, Canada;(2) Department of Mathematics and Statistics, University of Nebraska, 68588-0323 Lincoln, NE, USA |
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| Abstract: | The non-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the left regular representation of the free semigroup onn generators. We obtain a distance formula to an arbitrary WOT-closed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is used to obtain Nevanlinna-Pick type interpolation theoremsFirst author partially supported by an NSERC grant and a Killam Research Fellowship.Second author partially supported by an NSF grant. |
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| Keywords: | 47D25 |
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