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arXiv:1205.2025 [math.FA]AbstractReferencesReviewsResources

The numerical range of a contraction with finite defect numbers

Hari Bercovici, Dan Timotin

Published 2012-05-09Version 1

An n-dilation of a contraction T acting on a Hilbert space H is a unitary dilation acting on H \oplus C^n. We show that if both defect numbers of T are equal to n, then the closure of the numerical range of T is the intersection of the closures of the numerical ranges of its n-dilations. We also obtain detailed information about the geometrical properties of the numerical range of T in case n=1.

Categories: math.FA
Subjects: 47A12, 47A20
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