A bounded transform approach to self-adjoint operators: Functional calculus and affiliated von Neumann algebras
نویسندگان
چکیده
منابع مشابه
Torsion Theories for Algebras of Affiliated Operators of Finite Von Neumann Algebras
The dimension of any module over an algebra of affiliated operators U of a finite von Neumann algebra A is defined using a trace on A. All zero-dimensional U-modules constitute the torsion class of torsion theory (T,P). We show that every finitely generated U-module splits as the direct sum of torsion and torsion-free part. Moreover, we prove that the theory (T, P) coincides with the theory of ...
متن کاملStrongly 1-bounded Von Neumann Algebras
Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M . For α > 0, F is α-bounded if Pα(F ) < ∞ where Pα is the α-packing entropy of F introduced in [7]. We say that M is strongly 1-bounded if M has a 1-bounded finite set of selfadjoint generators F such that there exists an x ∈ F with χ(x) > −∞. It is shown that if M is strongly 1-bounded, then any finite set of ...
متن کاملDivisible Operators in Von Neumann Algebras
Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if W (x) ∩ M unitally contains a factor of type In. We decide the density of the n-divisible operators, for various n, M, and operator topologies. The most sensitive case is σ-strong density in II1 factors, which is closely related to the McDuff property. We make use of Voiculescu’s...
متن کاملInteger Operators in Finite Von Neumann Algebras
Motivated by the study of spectral properties of self-adjoint operators in the integral group ring of a sofic group, we define and study integer operators. We establish a relation with classical potential theory and in particular the circle of results obtained by M. Fekete and G. Szegö, see [Fek23,FS55,Sze24]. More concretely, we use results by R. Rumely, see [Rum99], on equidistribution of alg...
متن کاملA GEOMETRIC SPECTRAL THEORY FOR n-TUPLES OF SELF-ADJOINT OPERATORS IN FINITE VON NEUMANN ALGEBRAS: II
Given an n-tuple {b1, ..., bn} of self-adjoint operators in a finite von Neumann algebra M and a faithful, normal tracial state τ on M , we define a map Ψ from M to R by Ψ(a) = (τ(a), τ(b1a), . . . , τ(bna)). The image of the positive part of the unit ball under Ψ is called the spectral scale of {b1, .., bn} relative to τ and is denoted by B. In a previous paper with Nik Weaver we showed that t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Functional Analysis
سال: 2016
ISSN: 2008-8752
DOI: 10.1215/20088752-3605384