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Search: All articles in the CMB digital archive with keyword bounded operators

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1. CMB 2011 (vol 54 pp. 456)

Gustafson, Karl
On Operator Sum and Product Adjoints and Closures
We comment on domain conditions that regulate when the adjoint of the sum or product of two unbounded operators is the sum or product of their adjoints, and related closure issues. The quantum mechanical problem PHP essentially selfadjoint for unbounded Hamiltonians is addressed, with new results.

Keywords:unbounded operators, adjoints of sums and products, quantum mechanics
Category:47A05

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

3. CMB 2011 (vol 54 pp. 498)

Mortad, Mohammed Hichem
On the Adjoint and the Closure of the Sum of Two Unbounded Operators
We prove, under some conditions on the domains, that the adjoint of the sum of two unbounded operators is the sum of their adjoints in both Hilbert and Banach space settings. A similar result about the closure of operators is also proved. Some interesting consequences and examples "spice up" the paper.

Keywords:unbounded operators, sum and products of operators, Hilbert and Banach adjoints, self-adjoint operators, closed operators, closure of operators
Category:47A05

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