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arXiv · 1605.04115

Every synaptic algebra has the monotone square root property

David J. Foulis·Anna Jencova·Sylvia Pulmannova
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Abstract

A synaptic algebra is a common generalization of several ordered algebraic structures based on algebras of self-adjoint operators, including the self-adjoint part of an AW*-algebra. In this paper we prove that a synaptic algebra A has the monotone square property, i.e., if a and b are positive elements, then if a is less or equal than b, then the square root of a is less or equal than the square root of b.

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David J. Foulis, Anna Jencova, Sylvia Pulmannova. 2016-05-13. Every synaptic algebra has the monotone square root property. https://arxiv.org/abs/1605.04115

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