Generalized Wave Operators in Von Neumann Algebras

Let M?B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight r where B(H)is the set of all bound...     

On the Lower Bounds for Schatten-Von Neumann Norms of Certain Volterra Integral Operators

It is shown that the Schatten–von Neumann p-norm of aVolterra integral operator of the form is sandwiched, when 2 p < , by an integral expression similarto the well-known Hilbert–Schmidt norm.     

Principal Eigenvalues for Isaacs Operators with Neumann Boundary Conditions

In this paper we show the existence of two principal eigenvalues associated to general non-convex fully nonlinear elliptic operators with Neumann boundary conditions in a bounded C ² domain. We study these objects and we establish some of their basic properties. Finally, Lipschitz regularity, uniqueness and existence results for the solution of the Neumann problem are given.      

冯·诺依曼代数的可测算子的性质

本文研究了冯·诺依曼代数的可测算子的基本性质,定义了阶梯算子,证明了任意一个正可测算子可以由阶梯算子在定义域内按照强算子拓扑逼近,从而证明了任意一个可测算子可以由投影在定义域内按照强算子拓扑逼近.此外,还讨论了可测算子与有界算子的复合算子的可测性.     

Schatten-von Neumann Hankel Operators on the Bergman Space of Planar Domains

In this paper we study the problem of the joint membership of Hφ and in the Schatten-von Neumann p-class when φ ∈ L∞(Ω) and Ω is a planar domain. We use a result of K. Zhu and the localization near the boundary to solve the problem. Finally, we recover a result of Arazy, Fisher and Peetre on the case with φ holomorphic.      

On resonant Neumann problems

We consider semilinear Neumann problems at resonance and prove existence and multiplicity theorems. The existence theorems allow resonance with respect to any eigenvalue of the negative Neumann Laplacian. The multiplicity theorems concern problems resonant at 0 (the principal eigenvalue) or at the first nonzero eigenvalue. Our approach uses tools from critical point theory and from Morse theory.     

Maximal Abelian von Neumann Algebras and Toeplitz Operators with Separately Radial Symbols

This paper mainly concerns abelian von Neumann algebras generated by Toeplitz operators on weighted Bergman spaces. Recently a family of abelian w^*-closed Toeplitz algebras has been obtained (see [5,6,7,8]). We show that this algebra is maximal abelian and is singly generated by a Toeplitz operator with a “common” symbol. A characterization for Toeplitz operators with radial symbols is obtained and generalized to the high dimensional case. We give several examples for abelian von Neumann algebras in the case of high dimensional weighted Bergman spaces, which are different from the one dimensional case.     

Ideal Spaces of Measurable Operators Affiliated to A Semifinite Von Neumann Algebra

Suppose that M is a von Neumann algebra of operators on a Hilbert space H and τ is a faithful normal semifinite trace on M. Let E, F and G be ideal spaces on (M, τ). We find when a τ-measurable operator X belongs to E in terms of the idempotent P of M. The sets E+F and E·F are also ideal spaces on (M, τ); moreover, E·F = F·E and (E+F)·G = E·G+F·G. The structure of ideal spaces is modular. We establish some new properties of the L₁(M, τ) space of integrable operators affiliated to the algebra M. The results are new even for the *-algebra M = B(H) of all bounded linear operators on H which is endowed with the canonical trace τ = tr.     

On a problem of Neumann

A conjecture widely attributed to Neumann is that all finite non-desarguesian projective planes contain a Fano subplane. In this note, we show that any finite projective plane of even order which admits an orthogonal polarity contains many Fano subplanes. The number of planes of order less than $n$ previously known to contain a Fano subplane was $O(logn)$, whereas the number of planes of order less than $n$ that our theorem applies to is not bounded above by any polynomial in $n$.     

On von Neumann regular f-algebras

It is shown that for a large class of f-algebras, von Neumann regularity and -lateral completeness are equivalent notions.     

On Concave Operators

We prove that a u0-concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u0-concave operator under a weaker condition.     

On Ideal Operators

Let E, F be Archimedean Riesz spaces. We consider operators that map ideals of E to ideals of F and operators T for which, T ^–1 (I) is an ideal in E, for each ideal I in F. We study the properties of such operators and investigate their relation to disjointness preserving operators.     

On quasi-injectivity and von Neumann regularity

The purpose of this note is to consider certain connections between injectivity,p-injectivity and a generalisation of quasi-injectivity notedGQ-injectivity (cf. definition below). It is proved that ifA is a leftGQ-injective ring andZ the left singular ideal ofA, thenA/Z is von Neumann regular andZ is the Jacobson radical ofA (this extends the well-known result ofY. Utumi for left continuous rings [9]). If the sum of any twoGQ-injective leftA-modules isGQ-injective, thenA is a left Noetherian, left hereditary, leftV-ring. Semi-prime rings whose faithful left modules areGQ-injective must be semi-simple Artinian. IfA is commutative, the following are equivalent: (1)A is a finite direct sum of field; (2) EveryGQ-injectiveA-module is injective; (3) AnyA-module isGQ-injective if, and only if, it isp-injective; (4) AnyA-module is quasi-injective if, and only if, it isp-injective. Also, a commutative ringA is hereditary Noetherian if, and only if, the sum of any twop-injectiveA-modules is injective.     

On weakly injective von Neumann algebras

A von Neumann algebra \({M\subset B(H)}\) is called weakly injective if there exist an ultraweakly dense unital C*-subalgebra \({A\subset M}\) and a unital completely positive map φ : B(H) → M such that φ(a) = a for all \({a\in A}\). In this note we present several properties of weakly injective von Neumann algebras and highlight the role these algebras play in relation to the QWEP conjecture.