An inequality for spherical Cauchy dual tuples

Sameer 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 -