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arXiv · 1301.4252

Estimating Norms of Commutators

Terry A. Loring·Fredy Vides
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Abstract

We find estimates on the norms commutators of the form [f(x), y] in terms of the norm of [x, y] assuming that x and y are contractions in a C*-algebra A, with x normal and with spectrum within the domain of f. In particular we discuss [x^2, y] and [x^(1/2), y] for 0 <=, x <=, 1. For larger values of \delta = \|[x; y]\| we can rigorous calculate the best possible upper bound \|[f(x), y]\| for many f. In other cases we have conducted numerical experiments that strongly suggest that we have in many cases found the correct formula for the best upper bound.

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Terry A. Loring, Fredy Vides. 2013-01-17. Estimating Norms of Commutators. https://arxiv.org/abs/1301.4252

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