Factoriality of q-Gaussian von Neumann algebras

Approximate double commutants in von Neumann algebras

Richard Kadison showed that not every commutative von Neumann subalgebra of a factor von Neumann algebra is equal to its relative double commutant. We prove that every commutative C*-subalgebra of a centrally prime C*-algebra $B$ equals its relative approximate double commutant. If $B$ is a von Neumann algebra, there is a related distance formula.

Geometric characterizations of some classes of operators in C*-algebras and von Neumann algebras

We present geometric characterizations of the partial isometries, unitaries, and invertible operators in C*-algebras and von Neumann algebras.

A characterization of completely bounded normal Jordan $*$-homomorphisms on von Neumann algebras

We characterize completely bounded normal Jordan $*$-homomorphisms acting on von Neumann algebras. We also characterize completely positive isometries acting on noncommutative $\mathrm{L}^p$-spaces.

Complex interpolation of noncommutative Hardy spaces associated semifinite von Neumann algebra

We studied complex interpolation noncommutative Hardy space associated with semi-finite von Neumann algebra and extend Pisier's interpolation theorem for this case.

Semigroups in finite von Neumann algebras

Let $M$ be a finite von Neumann algebra. In the first part, we give asymptotic results about $M$-stable sequences of weak*-continuous mappings which are related with operators belonging to $M$. In the second part, we extend, by a shorter way, similarity results given in [CaFa2] to unbounded semigroups of operators contained in a finite von Neumann algebra.

从冯·诺伊曼代数到半单Banach代数的加性谱保持映射

Additive spectrum preserving mappings from von Neumann algebras

本文证明了Jafarian的猜想，即从冯·诺伊曼代数到半单巴拿赫代数的加性谱保持映射必然是若尔当同构。

Logarithmic submajorisations inequalities for operators in a finite von Neumann algebra

The aim of this paper is to study the logarithmic submajorisations inequalities for operators in a finite von Neumann algebra. Firstly, some logarithmic submajorisations inequalities due to Garg and Aulja are extended to the case of operators in a finite von Neumann algebra. As an application, we get some new Fuglede-Kadison determinant inequalities of operators in that circumstance. Secondly, we improve and generalize to the setting of finite von Neumann algebras, a generalized Hölder type generalized singular numbers inequality.

An example of a solid von Neumann algebra

We prove that the group-measure-space von Neumann algebra $L^\infty(T^2) \rtimes SL(2,Z)$ is solid. The proof uses topological amenability of the action of $SL(2,Z)$ on the Higson corona of $Z^2$.

Fundamental group of finite von Neumann algebras with finite dimensional normal trace space

We introduce the fundamental group $F(\mathcal{M})$ of a finite von Neumann algebra $\mathcal{M}$ with finite dimensional normal trace space. The form of $F(\mathcal{M})$ is completely determined. Moreover, there exists a finite von Neumann algebra $\mathcal{M}$ with finite dimensional normal trace space such that $F(\mathcal{M})=G$ for any conceivable groups $G$ as fundamental group.

The von Neumann algebra generated by t-gaussians

We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently close to 1, then these algebras do not depend on $t$. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.

Star order and topologies on von Neumann algebras

The goal of the 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 $σ$-strong* topology. On the other hand, we show that it is comparable with the norm topology if and only if the von Neumann algebra is finite-dimensional.

2-local $ (\upvarphi, \uppsi) $-Derivations on Finite von Neumann Algebras

In this paper, I introduce the concept of $ (\upvarphi, \uppsi) $-finite von Neumann algebras and I show that if $ \mathscr{M} $ is a finite and $ (\upvarphi, \uppsi) $-finite von Neumann algebra togather with condition $ \{ \big( Δ(u+v)-Δ(u)-Δ(v)\big)^{*}\} \subseteq \uppsi(\mathscr{M}) $, then each (approximately) 2-local $ (\upvarphi, \uppsi) $-derivation $ δ$ on $ \mathscr{M} $, is a $ (\upvarphi, \uppsi) $-derivation.

Structure of the time projection for stopping times in von Neumann algebras

We give an explicit formula for the time projection in an arbitrary von Neumann algebra from which all its basic properties can be easily derived. The analysis of the situation when this time projection is a conditional expectation is also performed.

Frobenius theory fails for semigroups of positive maps on von Neumann algebras

The eigenvectors of an ergodic semigroup of linear normal positive unital maps on a von Neumann algebra are described. Moreover, it is shown by means of examples, that mere positivity of the maps in question is not sufficient for Frobenius theory as in S. Albeverio and R. Høegh-Krohn, \emph{Frobenius theory of positive maps of von Neumann algebras}, Comm. Math. Phys. \bf{64}(1978), 83--94, to hold.

Co-representations of Hopf-von Neumann algebras on operator spaces other than column Hilbert space

Recently, M. Daws introduced a notion of co-representation of abelian Hopf--von Neumann algebras on general reflexive Banach spaces. In this note, we show that this notion cannot be extended beyond subhomogeneous Hopf--von Neumann algebras. The key is our observation that, for a von Neumann algebra $\M$ and a reflexive operator space $E$, the normal spatial tensor product $\M \bar{\tensor} \CB(E)$ is a Banach algebra if and only if $\M$ is subhomogeneous or $E$ is completely isomorphic to column Hilbert space.

On Markushevich bases in preduals of von Neumann algebras

We prove that the predual of any von Neumann algebra is $1$-Plichko, i.e., it has a countably $1$-norming Markushevich basis. This answers a question of the third author who proved the same for preduals of semifinite von Neumann algebras. As a corollary we obtain an easier proof of a result of U.~Haagerup that the predual of any von Neumann algebra enjoys the separable complementation property. We further prove that the self-adjoint part of the predual is $1$-Plichko as well.

Classification and rigidity for von Neumann algebras

In this talk, I will survey recent progress made on the classification of von Neumann algebras arising from countable groups and their actions on probability spaces. In particular, I will present the first results which provide classes of (superrigid) groups and actions that can be entirely reconstructed from their von Neumann algebras.

Rigidity for von Neumann algebras

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 (W$^*$-superrigid) actions that can be completely recovered from their von Neumann algebras and II$_1$ factors that have a unique Cartan subalgebra. We also present cocycle superrigidity theorems and some of their applications to orbit equivalence. Finally, we discuss several recent rigidity results for von Neumann algebras associated to groups.

Abelian von Neumann algebras, measure algebras and L^\infty-spaces

We give a fresh account of the astonishing interplay between abelian von Neumann algebras, L^\infty-spaces and measure algebras, including an exposition of Maharam's theorem from the von Neumann algebra perspective.

Isometric dilations and von Neumann inequality for a class of tuples in the polydisc

The celebrated Sz.-Nagy and Foias and Ando theorems state that a single contraction, or a pair of commuting contractions, acting on a Hilbert space always possesses isometric dilation and subsequently satisfies the von Neumann inequality for polynomials in $\mathbb{C}[z]$ or $\mathbb{C}[z_1, z_2]$, respectively. However, in general, neither the existence of isometric dilation nor the von Neumann inequality holds for $n$-tuples, $n \geq 3$, of commuting contractions. The goal of this paper is to provide a taste of the isometric dilations, the von Neumann inequality and a sharper version of von …

Generalized Von Neumann-Jordan Constant for Morrey Spaces and Small Morrey Spaces

In this paper we calculate some geometric constants for Morrey spaces and small Morrey spaces, namely generalized Von Neumann-Jordan constant, modified Von Neumann-Jordan constants, and Zbáganu constant. All these constants measure the uniformly nonsquareness of the spaces. We obtain that their values are the same as the value of Von Neumann-Jordan constant for Morrey spaces and small Morrey spaces.

On estimates of Schatten-von Neumann norms of Hardy-Steklov operator

Upper and lower estimates are obtained for the Schatten-von Neumann norms of the Hardy-Steklov operator in Lebesgue function spaces on the semi-axis.

Von Neumann's inequality for commuting operator-valued multishifts

Recently, Hartz proved that every commuting contractive classical multishift with non-zero weights satisfies the matrix-version of von Neumann's inequality. We show that this result does not extend to the class of commuting operator-valued multishifts with invertible operator weights. In particular, we show that if $A$ and $B$ are commuting contractive $d$-tuples of operators such that $B$ satisfies the matrix-version of von Neumann's inequality and $(1, \ldots, 1)$ is in the algebraic spectrum of $B$, then the tensor product $A \otimes B$ satisfies the von Neumann's inequality if and only if …

关于I型冯·诺依曼代数的近似顺从性的一个注记

A note on approximate amenability of type I von Neumann algebras

本文运用Ozawa与Runde的方法，证明了I型冯·诺依曼代数的近似顺从性与顺从性等价。

On some modifications of n-th von Neumann-Jordan constant for banach spaces

There are discussed some modifications of n-th von Neumann-Jordan constant considered by M. Kato, Y. Takahashi and K. Hashimoto. We study, among others, upper, lower, upper modified and lower modified n-th von Neumann-Jordan constant and relationships between them. There are characterized uniformly non-l_{n}^{1} Banach spaces in terms of the upper modified n-th von Neumann-Jordan constant. Moreover, this constant is calculated explicitly for Lebesgue spaces L^{p} and l^{p} (1\leq p\leq oo).

Some asymptotic estimates on the Von Neumann Inequality for homogeneous polynomials

We will discuss some results of the paper "Asymptotic estimates on the Von Neumann Inequality for homogeneous polynomials", of Galicer D., Muro S. and Sevilla-Peris P. Also, we will see how to extend some of these results using the same techniques in such paper.

Commutativity, majorization, and reduction in Fan-Theobald-von Neumann systems

A Fan-Theobald-von Neumann system is a triple $(V,W,λ)$, where $V$ and $W$ are real inner product spaces and $λ:V \to W$ is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decompositions systems (Eaton triples). In the previous paper (arXiv:1902.06640) we presented some basic properties of such systems and described results on optimization problems dealing with certain combinations of linear/distance and spectral functions…

冯·诺依曼代数中的部分追踪的詹森不等式

Jensen's inequality for partial traces in von Neumann algebras

本文在半有限冯·诺依曼代数中证明了部分追踪的詹森不等式，并扩展至一般冯·诺依曼代数框架。

On Schatten-von Neumann class properties of pseudo-differential operators. Boulkhemair's method

We investigate the Schatten-von Neumann properties of pseudo-differential operators using the method proposed by A. Boulkhemair in \cite{Boulkhemair 2}. The symbols are elements of the ideals $S_{w}^{p}$ of the Sjöstrand algebra $S_{w}$.

The automatic additivity of $ξ-$Lie derivations on von Neumann algebras

Let ${\mathcal M}$ be a von Neumann algebra with no central summands of type I$_1$. It is shown that every nonlinear $ξ-$Lie derivation ($ξ\neq 1$) on $\mathcal M$ is an additive derivation.

Some remarks on the Krein--von Neumann extension of different Laplacians

We discuss the Krein--von Neumann extensions of three Laplacian-type operators -- on discrete graphs, quantum graphs, and domains. In passing we present a class of one-dimensional elliptic operators such that for any $n\in \mathbb N$ infinitely many elements of the class have $n$-dimensional null space.

The Krein-von Neumann extension revisited

We revisit the Krein-von Neumann extension in the case where the underlying symmetric operator is strictly positive and apply this to derive the explicit form of the Krein-von Neumann extension for singular, general (i.e., three-coefficient) Sturm-Liouville operators on arbitrary intervals. In particular, the boundary conditions for the Krein-von Neumann extension of the strictly positive minimal Sturm-Liouville operator are explicitly expressed in terms of generalized boundary values adapted to the (possible) singularity structure of the coefficients near an interval endpoint.

A von Neumann theorem for uniformly distributed sequences of partitions

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.

Quantum smooth uncertainty principles for von Neumann bi-algebras

In this article, we prove various smooth uncertainty principles on von Neumann bi-algebras, which unify numbers of uncertainty principles on quantum symmetries, such as subfactors, and fusion bi-algebras etc, studied in quantum Fourier analysis. We also obtain Widgerson-Wigderson type uncertainty principles for von Neumann bi-algebras. Moreover, we give a complete answer to a conjecture proposed by A. Wigderson and Y. Wigderson.

An Infinitesimal Version of the Stone-von Neumann Theorem

In this paper, we present an infinitesimal version of the Stone-von Neumann Theorem. This work was motivated by the need to formulate the uniqueness property of the Heisenberg Commutation Relation purely in terms of unbounded operators.

A Remark on the structure of symmetric quantum dynamical semigroups on von Neumann algebras

We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of square of self-adjoint derivations of the von Neumann algebra. This generalizes some of the results obtained by Albeverio, H(phi)egh-Krohn and Olsen [Alb] for the special case of the finite dimensional ma…