Communications in Mathematical Analysis

Norm Estimates for Powers of Products of Operators in a Banach Space

Michael Gil’

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Abstract

Let $A$ and $B$ be bounded linear operators in a Banach space. We consider the following problem: if $\Sigma_{k=0}^{\infty} || A^{k} |||| B^{k} || \lt\infty$, under what conditions $\Sigma_{k=0}^{\infty} || (AB)^{k} || \lt \infty$?

Article information

Source
Commun. Math. Anal., Volume 20, Number 2 (2017), 1-7.

Dates
First available in Project Euclid: 3 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.cma/1509674425

Mathematical Reviews number (MathSciNet)
MR3721798

Zentralblatt MATH identifier
06841182

Subjects
Primary: 47A10: Spectrum, resolvent 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 15A42: Inequalities involving eigenvalues and eigenvectors

Keywords
Banach space powers of linear operators norm estimates

Citation

Gil’, Michael. Norm Estimates for Powers of Products of Operators in a Banach Space. Commun. Math. Anal. 20 (2017), no. 2, 1--7. https://projecteuclid.org/euclid.cma/1509674425


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