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- W2964333404 abstract "We prove that any map between projection lattices of AW⁎-algebras A and B, where A has no Type I2 direct summand, that preserves orthocomplementation and suprema of arbitrary elements, is a restriction of a normal Jordan ⁎-homomorphism between A and B. This allows us to generalize Dye's Theorem from von Neumann algebras to AW⁎-algebras. We show that Mackey–Gleason–Bunce–Wright Theorem can be extended to homogeneous AW⁎-algebras of Type I. The interplay between Dye's Theorem and Gleason's Theorem is shown. As an application we prove that Jordan ⁎-homomorphisms are commutatively determined. Another corollary says that Jordan parts of AW⁎-algebras can be reconstructed from posets of their abelian subalgebras." @default.
- W2964333404 created "2019-07-30" @default.
- W2964333404 creator A5091615681 @default.
- W2964333404 date "2015-02-01" @default.
- W2964333404 modified "2023-10-13" @default.
- W2964333404 title "Dye's Theorem and Gleason's Theorem for <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mi>A</mml:mi><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:math>-algebras" @default.
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- W2964333404 doi "https://doi.org/10.1016/j.jmaa.2014.09.040" @default.
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