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QUADRATIC INTEGRALS AND FACTORIZATION OF LINEAR OPERATORS

Published online by Cambridge University Press:  01 October 1997

GORDON BLOWER
GORDON BLOWER
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF
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Abstract

We consider operators on the matrix-valued disc algebra. We show that any bounded linear operator T: A[otimes ][Kscr ]→X to a Banach space X of cotype 2 induces a bounded operator Gν→X defined on some weighted Bergman space Gν on the unit disc. We give sufficient conditions on the weight ν for the formal inclusion A[otimes ][Kscr ]→Gν to be 2−C*-summing. Decompositions of T with respect to operator-valued measures are obtained.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 333 - 346
Copyright
The London Mathematical Society 1997

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