Some estimates for the norm of the self-commutator
Gevorgyan Levon
TL;DR
This paper presents new bounds for the norm of the self-commutator of a Hilbert space operator, including an upper bound related to the numerical range's area and an isoperimetric inequality.
Contribution
It introduces novel estimates for the self-commutator norm, notably linking it to the numerical range's area and establishing an isoperimetric inequality.
Findings
The self-commutator norm is bounded above by twice the numerical range area.
An isoperimetric inequality for the self-commutator norm is proved.
New bounds improve understanding of operator behavior in Hilbert spaces.
Abstract
Different estimates for the norm of the self-commutator of a Hilbert space operator are proposed. Particularly, this norm is bounded from above by twice of the area of the numerical range of the operator. An isoperimetric-type inequality is proved.
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Taxonomy
TopicsHolomorphic and Operator Theory · Spectral Theory in Mathematical Physics · Differential Equations and Boundary Problems