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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Towards a functional calculus for subnormal tuples: the minimal normal extension


Author: John B. Conway
Journal: Trans. Amer. Math. Soc. 326 (1991), 543-567
MSC: Primary 47B20; Secondary 32E30, 47A20, 47A60
MathSciNet review: 1005077
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Abstract: In this paper the study of a functional calculus for subnormal $ n$-tuples is initiated and the minimal normal extension problem for this functional calculus is explored. This problem is shown to be equivalent to a mean approximation problem in several complex variables which is solved. An analogous uniform approximation problem is also explored. In addition these general results are applied together with The Area and the The Coarea Formula from Geometric Measure Theory to operators on Bergman spaces and to the tensor product of two subnormal operators. The minimal normal extension of the tensor product of the Bergman shift with itself is completely determined.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1005077-X
PII: S 0002-9947(1991)1005077-X
Article copyright: © Copyright 1991 American Mathematical Society