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The Curvature of a Single Operator on a Hilbert Space

Stephen Parrott
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Abstract

This note studies Arveson's curvature invariant for d-contractions specialized to the case d=1 of a single contraction operator on a Hilbert space. It establishes a formula which gives an easy-to-understand meaning for the curvature of a single contraction. The formula is applied to give an example of an operator with nonintegral curvature. Under the additional hypothesis that the contraction T be "pure", we show that its curvature K(T) is given by K(T) = - index(T) := -(dim ker T - dim coker T).

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Stephen Parrott. 2000-06-29. The Curvature of a Single Operator on a Hilbert Space. https://arxiv.org/abs/math/0006224

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