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Estimating Norms of Commutators
Full text linkWe 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.Comment: We are posting the next version of this paper at :
http://repository.unm.edu/handle/1928/23462. Also posted at
http://repository.unm.edu is theMatlab code used to generate example
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