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Let $mathcal{M}$ be a von Neumann algebra, and let $0<p,qleinfty$. Then the space $Hom_mathcal{M}(L^p(mathcal{M}),L^q(mathcal{M}))$ of all right $mathcal{M}$-module homomorphisms from $L^p(mathcal{M})$ to $L^q(mathcal{M})$ is a reflexive subspace of the space of all continuous linear maps from $L^p(mathcal{M})$ to $L^q(mathcal{M})$. Further, the space $Hom_mathcal{M}(L^p(mathcal{M}),L^q(mathcal{M}))$ is hyperreflexive in each of the following cases: (i) $1le q<pleinfty$; (ii) $1le p,qleinfty$ and $mathcal{M}$ is injective, in which case the hyperreflexivity constant is at most $8$.
Let $mathcal{M}$ be a von Neumann algebra with a normal semifinite faithful trace $tau$. We prove that every continuous $m$-homogeneous polynomial $P$ from $L^p(mathcal{M},tau)$, with $0<p<infty$, into each topological linear space $X$ with the prope
Based on the characterization of surjective $L^p$-isometries of unitary groups in finite factors, we describe all surjective $L^p$-isometries between Grassmann spaces of projections with the same trace value in semifinite factors.
We show that the set of Schur idempotents with hyperreflexive range is a Boolean lattice which contains all contractions. We establish a preservation result for sums which implies that the weak* closed span of a hyperreflexive and a ternary masa-bimo
We apply Arvesons non-commutative boundary theory to dilate every Toeplitz-Cuntz-Krieger family of a directed graph $G$ to a full Cuntz-Krieger family for $G$. We do this by describing all representations of the Toeplitz algebra $mathcal{T}(G)$ that
An n-homomorphism between algebras is a linear map $phi : A to B$ such that $phi(a_1 ... a_n) = phi(a_1)... phi(a_n)$ for all elements $a_1, >..., a_n in A.$ Every homomorphism is an n-homomorphism, for all n >= 2, but the converse is false, in gener