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Generalized Effect Algebras of Positive Self-adjoint Linear Operators on Hilbert Spaces

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Abstract

In this paper, we introduce a partially defined binary operation on the set \(S^{+}(\mathcal {H})\) of all positive self-adjoint linear operators on a complex Hilbert space \(\mathcal {H}\), which makes the set into a generalized effect algebra. Moreover, we present two kinds of partial orders on \(S^{+}(\mathcal {H})\) and give the relationship of the two orders. We study two important topologies on \(S^{+}(\mathcal {H})\), too.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (Project 11101108), China Postdoctoral Science Foundation (Project 2011M500646) and Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (Project 2011008).

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Qiang Lei

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Junde Wu

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  1. Qiang Lei
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  2. Junde Wu
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Correspondence to Qiang Lei.

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Lei, Q., Wu, J. Generalized Effect Algebras of Positive Self-adjoint Linear Operators on Hilbert Spaces. Int J Theor Phys 53, 3981–3987 (2014). https://doi.org/10.1007/s10773-014-2149-y

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  • DOI: https://doi.org/10.1007/s10773-014-2149-y

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