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Quantum State Preparation Representation Quantum Simulation Entanglement Theory Quantum Correlations Topological Quantum Computing

Relatively bounded operators and the operator E-norms (addition to arXiv:1806.05668)

arXiv
Authors: M. E. Shirokov

Year

2018

Paper ID

23159

Status

Preprint

Abstract Read

~2 min

Abstract Words

121

Citations

N/A

Abstract

In this brief note we describe relations between the well known notion of a relatively bounded operator and the operator E-norms considered in [arXiv:1806.05668]. We show that the set of all sqrt{G}-bounded operators equipped with the E-norm induced by a positive operator G is the Banach space of all operators with finite E-norm and that the sqrt{G}-bound is a continuous seminorm on this space. We also show that the set of all sqrt{G}-infinitesimal operators operators with zero $sqrt{G}$-bound equipped with the E-norm induced by a positive operator G is the completion of the algebra B(H) of bounded operators w.r.t. this norm. Some properties of sqrt{G}-infinitesimal operators are considered.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • In this brief note we describe relations between the well known notion of a relatively bounded operator and the operator E-norms considered in [arXiv:1806.05668].

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1811.09659 [2] arXiv https://arxiv.org/abs/1811.09659 [3] Publisher https://arxiv.org/abs/1811.09659

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