An inequality for spherical Cauchy dual tuples

Sameer Chavan

Sameer Chavan

Colloquium Mathematicae, Tome 131 (2013), p. 265-271 / Harvested from The Polish Digital Mathematics Library

Résumé

Let T be a spherical 2-expansive m-tuple and let $T^{}$ denote its spherical Cauchy dual. If $T^{}$ is commuting then the inequality $\binom{\sum_{| β | = k} {(β!)}^{- 1} {(T^{})}^{β} (T^{}) *^{β} \leq (k + m - 1}{k) \sum_{| β | = k} {(β!)}^{- 1} (T^{}) *^{β} {(T^{})}^{β}}$ 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.

Publié le : 2013-01-01

Zbl 1296.47006

EUDML-ID : urn:eudml:doc:283552

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     title = {An inequality for spherical Cauchy dual tuples},
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     volume = {131},
     year = {2013},
     pages = {265-271},
     zbl = {1296.47006},
     language = {en},
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Sameer Chavan. An inequality for spherical Cauchy dual tuples. Colloquium Mathematicae, Tome 131 (2013) pp. 265-271. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-2-8/