Star Order and Topologies on von Neumann Algebras
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DOI: 10.1007/s00009-018-1221-x
Abstract: The goal of this paper is to study a topology generated by the star order on von Neumann algebras. In particular, it is proved that the order topology under investigation is finer than $$\sigma $$σ-strong*… read more here.
Keywords: neumann algebras; star order; order topologies; topology ... See more keywords
Representations of von Neumann Algebras and Ultraproducts
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DOI: 10.1007/s10773-019-04318-x
Abstract: We will introduce the concept of ergodicity of states with respect to some group of transformations on a von Neumann algebra and its properties are studied. A connection between the ergodic states on the von… read more here.
Keywords: algebras ultraproducts; representations von; neumann algebras; von neumann ... See more keywords
Mappings Preserving Sum of Products $$a\circ b-ba^{*}$$a∘b-ba∗ on Factor von Neumann Algebras
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DOI: 10.1007/s41980-020-00406-5
Abstract: Let $$\mathcal {A}$$ and $$\mathcal {B}$$ be two factor von Neumann algebras. In this paper, we proved that a bijective mapping $$\varPhi :\mathcal {A}\rightarrow \mathcal {B}$$ satisfies $$\varPhi (a\circ b-ba^{*})=\varPhi (a)\circ \varPhi (b)-\varPhi (b)\varPhi (a)^{*}$$… read more here.
Keywords: factor von; neumann algebras; von neumann; varphi ... See more keywords
A Gromov-Hausdorff distance between von Neumann algebras and an application to free quantum fields
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DOI: 10.1016/j.jfa.2016.12.029
Abstract: Abstract A distance between von Neumann algebras is introduced, depending on a further norm inducing the w ⁎ -topology on bounded sets. Such notion is related both with the Gromov–Hausdorff distance for quantum metric spaces… read more here.
Keywords: quantum; distance von; neumann algebras; topology ... See more keywords
Notes on derivations of Murray–von Neumann algebras
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DOI: 10.1016/j.jfa.2020.108589
Abstract: Abstract Let M be a type II1 von Neumann factor and let S ( M ) be the associated Murray-von Neumann algebra of all measurable operators affiliated to M . We extend a result of… read more here.
Keywords: notes derivations; neumann algebras; murray von; derivation ... See more keywords
Tingley's problem on finite von Neumann algebras
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DOI: 10.1016/j.jmaa.2017.02.013
Abstract: Abstract In this paper, we give an affirmative answer to Tingley's problem between finite von Neumann algebras. To do this, we see that every norm closed proper face of the unit ball of a unital… read more here.
Keywords: tingley problem; neumann algebras; problem finite; finite von ... See more keywords
Spectral properties of Markov semigroups in von Neumann algebras
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DOI: 10.1016/j.jmaa.2017.04.029
Abstract: Abstract We investigate spectral properties of Markov semigroups in von Neumann algebras and their dual semigroups in a fairly general setting which assumes only the abelianess of the semigroups and positivity of the maps in… read more here.
Keywords: properties markov; neumann algebras; spectral properties; markov semigroups ... See more keywords
On the extension of isometries between the unit spheres of von Neumann algebras
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DOI: 10.1016/j.jmaa.2018.05.062
Abstract: We prove that every surjective isometry between the unit spheres of two von Neumann algebras admits a unique extension to a surjective real linear isometry between these two algebras. read more here.
Keywords: extension isometries; unit spheres; neumann algebras; von neumann ... See more keywords
LEFT SYMMETRIC POINTS FOR BIRKHOFF ORTHOGONALITY IN THE PREDUALS OF VON NEUMANN ALGEBRAS
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DOI: 10.1017/s0004972718000849
Abstract: In this paper, we give a complete description of left symmetric points for Birkhoff orthogonality in the preduals of von Neumann algebras. As a consequence, except for $\mathbb{C}$ , $\ell _{\infty }^{2}$ and $M_{2}(\mathbb{C})$ ,… read more here.
Keywords: neumann algebras; points birkhoff; birkhoff orthogonality; symmetric points ... See more keywords
Quantumf-divergences in von Neumann algebras. I. Standardf-divergences
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DOI: 10.1063/1.5039973
Abstract: We make a systematic study of standard $f$-divergences in general von Neumann algebras. An important ingredient of our study is to extend Kosaki's variational expression of the relative entropy to an arbitary standard $f$-divergence, from… read more here.
Keywords: algebras standardf; neumann algebras; divergences von; quantumf divergences ... See more keywords
Ueda’s peak set theorem for general von Neumann algebras
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DOI: 10.1090/tran/7275
Abstract: We extend Ueda's peak set theorem for subdiagonal subalgebras of tracial finite von Neumann algebras, to sigma-finite von Neumann algebras (that is, von Neumann algebras with a faithful state; which includes those on a separable… read more here.
Keywords: neumann algebras; peak set; set theorem; ueda peak ... See more keywords