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arXiv · 1512.04979

Commutator inequalities via Schur products

Erik Christensen
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Abstract

For a self-adjoint unbounded operator D on a Hilbert space H, a bounded operator y on H and some complex Borel functions g(t) we establish inequalities of the type ||[g(D),y]|| \leq A|||y|| + B||[D,y]|| + ...+ X|[D, [D,...[D, y]...]]||. The proofs take place in a space of infinite matrices with operator entries, and in this setting it is possible to approximate the matrix associated to [g(D), y] by the Schur product of a matrix approximating [D,y] and a scalar matrix. A classical inequality of Bennett on the norm of Schur products may then be applied to obtain the results.

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BibTeXRIS

Erik Christensen. 2015-12-15. Commutator inequalities via Schur products. https://arxiv.org/abs/1512.04979

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