Every synaptic algebra has the monotone square root property |
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| Authors: | David J Foulis Anna Jenčová Sylvia Pulmannová |
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| Institution: | 1.Emeritus Professor, Department of Mathematics and Statistics,University of Massachusetts,Amherst,USA;2.Mathematical Institute,Slovak Academy of Sciences,Bratislava,Slovakia |
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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 root property, i.e., if \(0\le a,b\in A\), then \(a\le b \Rightarrow a^{1/2}\le b^{1/2}\). |
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