Let M be a von Neumann algebra, and let 0<p,q≤∞. Then the space HomM(Lp(M),Lq(M)) of all right M-module homomorphisms from Lp(M) to Lq(M) is a reflexive subspace of the space of all continuous linear ...maps from Lp(M) to Lq(M). Further, the space HomM(Lp(M),Lq(M)) is hyperreflexive in each of the following cases: (i) 1≤q<p≤∞; (ii) 1≤p,q≤∞ and M is injective, in which case the hyperreflexivity constant is at most 8.
We study the question of how quickly products of a fixed conjugacy class in the projective unitary group of a II1-factor von Neumann algebra cover the entire group. Our result is that the number of ...factors that are needed is essentially as small as permitted by the 1-norm – in analogy to results of Liebeck and Shalev for non-abelian finite simple groups. As an application of the techniques, we prove that every homomorphism from the projective unitary group of a finite factor to a Polish SIN group is continuous – a result which is even new for PU(n). Moreover, we show that the projective unitary group of a II1-factor carries a unique Polish group topology.
Let M be a properly infinite semifinite factor and n≥1. For each 1≤i≤n, let Lpi,1(M) be a Lorentz (pi,1)-ideal of M, where p1,…,pn are real numbers satisfying 1≤p1,…,pn<∞ and ∑i=1npi−1≤1. Assuming ...that the spectral measure of a commuting self-adjoint n-tuple (α(i))i=1n∈Mn is singular, we prove that there exists a commuting self-adjoint diagonal n-tuple (δ(i))i=1n∈Mn such that α(i)−δ(i)∈Lpi,1(M), 1≤i≤n. Moreover, max1≤i≤nmax{‖α(i)−δ(i)‖Lpi,1(M),‖α(i)−δ(i)‖M} can be arbitrarily small. This extends an earlier result due to Voiculescu.
For H a closed group of a locally compact group G, B. Forrest (4) has defined the Fourier and Fourier Stieltjes algebras associated to the coset space G/H, A(G/H) and B(G/H) respectively. He proved ...that when H is compact, it is possible to extend many classical results to this new setting. We continue this investigation with the study of the dual space of A(G/H), showing that it can be identified with a particular type of w⁎-closed ideal of VN(G) determined by H. We obtain a characterization of all w⁎-closed left ideals of VN(G) that are of this particular form. We introduce and study the analogs of some of the classical subspaces of VN(G), UBC(Gˆ), W(Gˆ) and AP(Gˆ) in the new setting. We obtain results similar to those of D.E. Ramirez (2), E. Granirer (6) and A.T. Lau (9) obtained for these spaces in the group setting.
Gleason’s theorem for composite systems Frembs, Markus; Döring, Andreas
Journal of physics. A, Mathematical and theoretical,
11/2023, Volume:
56, Issue:
44
Journal Article
We prove that the negative generator L of a semigroup of positive contractions on L∞ has bounded H∞(Sη)-calculus on the associated Poisson semigroup-BMO space for any angle η>π/2, provided L ...satisfies Bakry-Émery's Γ2≥0 criterion. Our arguments only rely on the properties of the underlying semigroup and work well in the noncommutative setting. A key ingredient of our argument is a type of quasi monotone properties for the subordinated semigroup Tt,α=e−tLα,0<α<1, that is proved in the first part of this article.
Lie-type maps on -algebras Nascimento Ferreira, Ruth; Macedo Ferreira, Bruno Leonardo; Guzzo Junior, Henrique ...
Communications in algebra,
12/2/2022, Volume:
50, Issue:
12
Journal Article
Peer reviewed
Let
and
be two
-algebras with identities
and
respectively, and P
1
and
nontrivial symmetric projections in
In this paper, we study the characterization of multiplicative
-Lie-type maps. In ...particular, if
is a factor von Neumann algebra then every complex scalar multiplication bijective unital multiplicative
-Lie-type map is
-isomorphism.
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