منابع مشابه
Estimating Norms of Commutators
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 contactions in a C*-algebra A, with x normal and with spectrum within the domain of f . In particular we discuss ‖[x, y]‖ and ‖[x, y]‖ for 0 ≤ x ≤ 1. For larger values of δ = ‖[x, y]‖ we can rigorous calculate the best possible upper bound ‖[f(x), y]‖ ≤ ηf (δ) for many f . ...
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The singular values of XY − Y X are the objects under investigation. Here, X and Y are square matrices with complex entries, and one of them has rank one. Hence, there are at most two non-trivial numbers among the commutator’s singular values, and the pairs of interest can be depicted in the plane. The emphasis will lie on the unexpectedly intriguing case in which both matrices are of rank one ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.10.042