An inequality for spherical Cauchy dual tuples

• Autorzy: Sameer Chavan
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 47A65: Structure theory
• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
• 47B20: Subnormal operators, hyponormal operators, etc.
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 131
• Numer: 2
• Strony: 265-271

Daty

wydano

2013

Twórcy

autor

Sameer Chavan

• Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur 208016, India

Identyfikatory

DOI

10.4064/cm131-2-8