Related papers: Conditional expectations onto maximal abelian *-su…
We obtain subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces embedded in $\mathbb{C}^n$ with isolated singularities. $W^{\epsilon}$ Sobolev norms of a form, $f$, for $0< \epsilon < 1$ are estimated in terms…
The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra…
Given any irreducible inclusion $\mB \subset \mA$ of unital $C^*$-algebras with a finite-index conditional expectation $E: \mA \to \mB$, we show that the set of $E$-compatible intermediate $C^*$-subalgebras is finite, thereby generalizing a…
In this paper, the main objective is to compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional supersolvable Lie algebras. We characterise the maximal abelian subalgebras of solvable Lie algebras and study…
We provide a self-contained proof of the Artin-Wedderburn theorem in the case of finite-dimensional Von Neumann algebras (or equivalently unital C* algebras) that is fully constructive and uses only basic notions of linear algebra.
We generalize the existence of maximal orders in a semi-simple algebra for general ground rings. We also improve several statements in Chapter 5 and 6 of Reiner's book concerning separable algebras by removing the separability condition,…
We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize results which provide classes of…
We propose a construction of quantum hypergroups using conditional expectations on compact quantum groups. Using this construction, we describe several series of non-trivial finite-dimensional quantum hypergroups via conditional…
In this article, we give explicit examples of maximal amenable subalgebras of the $q$-Gaussian algebras, namely, the generator subalgebra is maximal amenable inside the $q$-Gaussian algebras for real numbers $q$ with its absolute value…
Ge asked the question whether $LF_{\infty}$ can be embedded into $LF_2$ as a maximal subfactor. We answer it affirmatively by three different approaches, all containing the same key ingredient: the existence of maximal subgroups with…
We show that standard deviation $\s$ satisfies the Leibniz inequality $\s(fg) \leq \s(f)\|g\| + \|f\|\s(g)$ for bounded functions f, g on a probability space, where the norm is the supremum norm. A related inequality that we refer to as…
According to J. Feldman and C. Moore's well-known theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and…
We show that a given set of first class constraints becomes abelian if one maps each constraint to the surface of other constraints. There is no assumption that first class constraints satisfy a closed algebra. The explicit form of the…
The main purpose of this paper is to construct *-representations from unbounded C$^*$-seminorms on partial *-algebras and to investigate their *-representations.
In this paper, we introduce a new type of backward stochastic differential equations (BSDEs), called conditional expectation BSDEs, whose drivers depend not only on the value of the solutions but also on their conditional expectations with…
The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is…
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 Hilbert…
Motivated by Arveson's conjecture, we introduce a notion of hyperrigidity for a partial order on the state space of a $C^*$-algebra $B$. We show how this property is equivalent to the existence of a boundary: a subset of the pure states…
A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite…
We shall introduce the notions of the strong Morita equivalence for unital inclusions of unital $C^*$-algebras and conditional expectations from an equivalence bimodule onto its closed subspace with respect to conditional expectations from…