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A Non-commutative Yosida–Hewitt Theorem and Convex Sets of Measurable Operators Closed Locally in Measure

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Abstract

We present a non-commutative extension of the classical Yosida–Hewitt decomposition of a finitely additive measure into its σ-additive and singular parts. Several applications are given to the characterisation of bounded convex sets in Banach spaces of measurable operators which are closed locally in measure.

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Authors and Affiliations

  1. School of Informatics and Engineering, The Flinders University of South Australia, GPO Box 2100, Adelaide, SA, 5001, Australia

    P. G. Dodds, T. K. Dodds & F. A. Sukochev

  2. Research Institute of Mathematics and Mechanics, Kazan State University, Universitetskaya Str.17, Kazan, Tatarstan, 420008, Russia

    O. Ye. Tikhonov

Authors
  1. P. G. Dodds
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  2. T. K. Dodds
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  3. F. A. Sukochev
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  4. O. Ye. Tikhonov
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Corresponding author

Correspondence to P. G. Dodds.

Additional information

Dedicated to the memory of A. C. Zaanen and Y. Ja. Abramovich.

Mathematics Subject Classification (2000): Primary 46L52, Secondary 46E30, 47B55

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Dodds, P.G., Dodds, T.K., Sukochev, F.A. et al. A Non-commutative Yosida–Hewitt Theorem and Convex Sets of Measurable Operators Closed Locally in Measure. Positivity 9, 457–484 (2005). https://doi.org/10.1007/s11117-005-1384-0

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  • DOI: https://doi.org/10.1007/s11117-005-1384-0

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