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Matrix norm inequalities and the relative Dixmier property

✍ Scribed by Kenneth Berman; Herbert Halpern; Victor Kaftal; Gary Weiss

Publisher
SP Birkhäuser Verlag Basel
Year
1988
Tongue
English
Weight
906 KB
Volume
11
Category
Article
ISSN
0378-620X

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📜 SIMILAR VOLUMES

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Let N/M be an inclusion of von Neumann algebras with a conditional expectation E: M Ä N satisfying the finite index condition of [PiPo], i.e., there exists c>0 such that E(x) cx, \x # M + . In [Po4] we proved that such inclusions N/M satisfy the relative version of Dixmier's property, namely for any

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We show that a certain matrix norm ratio studied by Parlett has a supremum that is O(&) when the chosen norm is the Frobenius norm, while it is O(1og n) for the 2-norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n matrix.