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An inequality for spherical Cauchy dual tuples

Sameer Chavan (2013)

Colloquium Mathematicae

Let T be a spherical 2-expansive m-tuple and let T denote its spherical Cauchy dual. If T is commuting then the inequality | β | = k ( β ! ) - 1 ( T ) β ( T ) * β ( k + m - 1 k ) | β | = k ( β ! ) - 1 ( T ) * β ( T ) β holds for every positive integer k. In case m = 1, this reveals the rather curious fact that all positive integral powers of the Cauchy dual of a 2-expansive (or concave) operator are hyponormal.

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