Communications in Mathematical Analysis

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

Michael Gil’

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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

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

First available in Project Euclid: 3 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Banach space powers of linear operators norm estimates


Gil’, Michael. Norm Estimates for Powers of Products of Operators in a Banach Space. Commun. Math. Anal. 20 (2017), no. 2, 1--7.

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