New formulas for the spectral radius via Aluthge transform
Fadil Chabbabi, Mostafa Mbekhta (LPP)
TL;DR
This paper introduces new formulas for calculating the spectral radius of bounded operators on Hilbert spaces using Aluthge transforms, numerical radius, and operator power behavior, along with characterizations of normaloid operators.
Contribution
It provides novel expressions and characterizations connecting spectral radius, Aluthge transforms, and normaloid operators, advancing operator theory understanding.
Findings
Spectral radius expressed via Aluthge iterates
Characterizations of normaloid operators
Relationships between numerical radius and spectral properties
Abstract
In this paper we give several expressions of spectral radius of a bounded operator on a Hilbert space, in terms of iterates of Aluthge transformation, numerical radius and the asymptotic behavior of the powers of this operator. Also we obtain several characterizations of normaloid operators.
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Taxonomy
TopicsHolomorphic and Operator Theory · Matrix Theory and Algorithms · Spectral Theory in Mathematical Physics