# An inequality for spherical Cauchy dual tuples

Colloquium Mathematicae (2013)

- Volume: 131, Issue: 2, page 265-271
- ISSN: 0010-1354

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topSameer Chavan. "An inequality for spherical Cauchy dual tuples." Colloquium Mathematicae 131.2 (2013): 265-271. <http://eudml.org/doc/283552>.

@article{SameerChavan2013,

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

author = {Sameer Chavan},

journal = {Colloquium Mathematicae},

keywords = {jointly hyponormal; spherical 2-expansion; Cauchy dual},

language = {eng},

number = {2},

pages = {265-271},

title = {An inequality for spherical Cauchy dual tuples},

url = {http://eudml.org/doc/283552},

volume = {131},

year = {2013},

}

TY - JOUR

AU - Sameer Chavan

TI - An inequality for spherical Cauchy dual tuples

JO - Colloquium Mathematicae

PY - 2013

VL - 131

IS - 2

SP - 265

EP - 271

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

LA - eng

KW - jointly hyponormal; spherical 2-expansion; Cauchy dual

UR - http://eudml.org/doc/283552

ER -

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