Related papers: Conditional expectations onto maximal abelian *-su…

We construct a singly generated subalgebra of ${\mathcal K}({\mathcal H})$ which is non-amenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly…

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a…

A notion of partial ideal for an operator algebra is a weakening the notion of ideal where the defining algebraic conditions are enforced only in the commutative subalgebras. We show that, in a von Neumann algebra, the ultraweakly closed…

Let $j:Y \to X$ be a continuous surjection of compact metric spaces. Whyburn proved that $j$ is irreducible, meaning that $j(F) \subsetneq X$ for any proper closed subset $F \subsetneq Y$, if and only if $j$ is almost one-to-one, in the…

It is well known that elliptic estimates fail for the $\bar\partial$-Neumann problem. Instead, the best that one can hope for is that derivatives in every direction but one can be estimated by the associated Dirichlet form, and when this…

Let $(M, \varphi) = (M_1, \varphi_1) \ast (M_2, \varphi_2)$ be the free product of any $\sigma$-finite von Neumann algebras endowed with any faithful normal states. We show that whenever $Q \subset M$ is a von Neumann subalgebra with…

It is shown that the *-algebra of all (closed densely defined linear) operators affiliated with a finite type I von Neumann algebra admits a unique center-valued trace, which turns out to be, in a sense, normal. It is also demonstrated that…

For a maximal abelian subalgebra $A\subset M$ in a finite von Neumann algebra, we consider an invariant due to Takesaki which is an equivalence relation on a standard probability space. We give several characterization of this invariant and…

We find necessary and sufficient conditions for the subalgebra of analytic elements associated with a periodic C*-dynamical system to be a maximal norm-closed subalgebra. Our conditions are in terms of the Arveson spectrum of the action. We…

We prove that an inclusion $\mathcal{B} \subset \mathcal{A}$ of simple unital $C^*$-algebras with a finite-index conditional expectation is regular if and only if there exists a finite group $G$ that admits a cocycle action…

In this note, we derive some consequences of the von Neumann algebra uniqueness theorems developed in a previous paper (see arXiv:1207.6741v1). In particular, 1) we solvein a paper of Futamura, Kataoka, and Kishimoto, by proving that if A…

We introduce the notion of a C*-valued weight between two C*-algebras as a generalization of an ordinary weight on a C*-algebra and as a C*-version of operator valued weights on von Neumann algebras. Also, some form of lower semi-continuity…

It is known that every semigroup of normal completely positive maps of a von Neumann can be ``dilated" in a particular way to an E_0-semigroup acting on a larger von Neumann algebra. The E_0-semigroup is not uniquely determined by the…

An operator $T$ in a separable factor $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann subalgebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$.…

We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras $M = M_1 \ast_B M_2$. Our main result states that under natural analytic assumptions, any amenable subalgebra of $M$ that has a…

In this paper, we establish a globally quantitative estimate of unique continuation at one time point for solutions of parabolic equations with Neumann boundary conditions in bounded domains. Our proof is mainly based on Carleman commutator…

The aim of this article is to describe a class of *-algebras that allows to treat well-behaved algebras of unbounded operators independently of a representation. To this end, Archimedean ordered *-algebras (*-algebras whose real linear…

We examine a certain type of abelian C*-subalgebras that allow one to give a unified treatment of two uniqueness theorems: for graph C*-algebras and for certain reduced crossed products.

This is a PhD thesis about generated Jacobian equations; our purpose is twofold. First, we provide an introduction to these equations, whilst, at the same time, collating some results scattered throughout the literature. The other goal is…

We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside $\mathbb{Z}^2 \rtimes SL_2(\mathbb{Z})$ and obtain several explicit instances…