We prove that the type factor generated by the regular representation of is isomorphic to its tensor product with the hyperfinite type factor. This implies that the unitary group of is contractible with respect to the topology defined by the natural Hilbertian norm.
Let G be the set of invertible elements of a normed algebra A with an identity. For some but not all subsets H of G we have the following dichotomy. For x ∈ A either for all c ∈ H or . In that case the set of x ∈ A for which the sup is finite is the centralizer of H.
It is shown that every von Neumann algebra whose centre determines the state space is already abelian.
In this paper we deal with Cesàro wedge and weak Cesàro wedge -spaces, and give several characterizations. Some applications of these spaces to general summability domains are also studied.
Článek je věnován genezi pojmu kompaktního operátoru. Cesta k jeho vytvoření trvala několik desetiletí a nebyla přímočará. Od problémů fyziky k jejich matematické formulaci pomocí integrálních rovnic, přes okrajové úlohy teorie potenciálu, přes snahy o řešení nekonečných soustav lineárních rovnic. Cesta ilustruje ideu přechodu od konečného k nekonečnému, od diskrétního ke spojitému. Ukazuje, proč a jak matematika dospěla k funkcím nekonečně mnoha proměnných, k prostorům funkcí a obecněji, k nekonečněrozměrným...
In previous papers we introduced and studied the extension of a state defined on a von Neumann subalgebra to the whole of the von Neumann algebra with respect to a given state. This was done by using the standard form of von Neumann algebras. In the case of the existence of a norm one projection from the algebra to the subalgebra preserving the given state our construction is simply equivalent to taking the composition with the norm one projection. In this paper we study couples of von Neumann subalgebras...
In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We only need...
The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
A brief introduction to -graded quantum stochastic calculus is given. By inducing a superalgebraic structure on the space of iterated integrals and using the heuristic classical relation df(Λ) = f(Λ + dΛ) - f(Λ) we provide an explicit formula for chaotic expansions of polynomials of the integrator processes of -graded quantum stochastic calculus.
We study the notion of character Connes amenability of dual Banach algebras and show that if is an Arens regular Banach algebra, then is character Connes amenable if and only if is character amenable, which will resolve positively Runde’s problem for this concept of amenability. We then characterize character Connes amenability of various dual Banach algebras related to locally compact groups. We also investigate character Connes amenability of Lau product and module extension of Banach algebras....
Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.
Let be the wreath product of a compact group T with the infinite symmetric group . We study the characters of factor representations of finite type of G, and give a formula which expresses all the characters explicitly.
Character inner amenability for a certain class of Banach algebras including projective tensor products, Lau products and module extensions is investigated. Some illuminating examples are given.
Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We introduce and study a new notion of amenability for 𝓐 based on existence of a ϕ-approximate diagonal by modifying the concepts of ϕ-amenability and pseudo-amenability. We then apply these results to characterize ϕ-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue-Fourier algebras.