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Search: MSC category 47B99 ( None of the above, but in this section )

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1. CMB Online first

Rhaly, H. C.
Corrigendum to "Generalized Cesàro Matrices"
This note corrects an error in Theorem 1 of "Generalized Cesàro matrices" Canad. Math. Bull. 27 (1984), no. 4, 417-422.

Keywords:Cesaro operator, Hilbert-Schmidt operator, numerical range
Categories:47B99, 47A12, 47B10, 47B38

2. CMB 2011 (vol 55 pp. 339)

Loring, Terry A.
From Matrix to Operator Inequalities
We generalize Löwner's method for proving that matrix monotone functions are operator monotone. The relation $x\leq y$ on bounded operators is our model for a definition of $C^{*}$-relations being residually finite dimensional. Our main result is a meta-theorem about theorems involving relations on bounded operators. If we can show there are residually finite dimensional relations involved and verify a technical condition, then such a theorem will follow from its restriction to matrices. Applications are shown regarding norms of exponentials, the norms of commutators, and "positive" noncommutative $*$-polynomials.

Keywords:$C*$-algebras, matrices, bounded operators, relations, operator norm, order, commutator, exponential, residually finite dimensional
Categories:46L05, 47B99

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