Commutators in Properly Infinite Von Neumann Algebras
نویسندگان
چکیده
منابع مشابه
Various topological forms of Von Neumann regularity in Banach algebras
We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...
متن کاملVanishing of the Cyclic Cohomology of Infinite Von Neumann Algebras
We prove that if A is an infinite von Neumann algebra (i. e., the identity can be decomposed as a sum of a sequence of pairwise disjoint projections, all equivalent to the identity) then the cyclic cohomology of A vanishes. We show that the method of the proof applies to certain algebras of infinite matrices.
متن کاملvon Neumann Algebras
For every selfadjoint operator T in the Hilbert space H, f(T) makes sense not only in the obvious case where / is a polynomial but also if / is just measurable, and if fn(x)-+f(x) for all x£R (with (/,) bounded) then fn(T)-+f(T) weakly, i.e. <fn(T)£9i)+<f(T)£9ti)V£9fiCH. Moreover the set {f(T)9 f measurable} is the set of all operators S in H invariant under all unitary transformations of H whi...
متن کاملVon Neumann Algebras
The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. In this sense it is opposite in spirit from the treatises of Dixmier [], Takesaki[], Pedersen[], Kadison-Ringrose[], Stratila-Zsido[]. The philosophy is to lavish attention on a few key results and examples, and we prefer to make...
متن کاملNonlinear $*$-Lie higher derivations on factor von Neumann algebras
Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.
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: Transactions of the American Mathematical Society
سال: 1969
ISSN: 0002-9947
DOI: 10.2307/1995306