Search results for "algebra"
showing 10 items of 4129 documents
MR3730338 Reviewed de Jeu, Marcel(NL-LEID-MI); Tomiyama, Jun(J-TOKYM) The closure of ideals of ℓ1(Σ) in its enveloping C∗-algebra. (English summary) …
2018
Given a compact Hausdorff space X and a homeomorphism σ on X, denote by Σ=(X,σ) a topological dynamical system. Then the associated Banach ∗-algebra ℓ1(Σ) is defined as ℓ1(Σ)={a:Z→C(X), ∥a∥:=∑n∈Z∥a(n)∥<∞} with a crossed product–type product (aa′)(n)=∑k∈Za(k)⋅αk(a′(n−k)) and involution a∗(n)=αn(a(−n))¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯, where C(X) denote the space of complex-valued continuous functions on X, and α(f):=f∘σ−1 for f∈C(X). If C∗(Σ) is the enveloping C∗-algebra of ℓ1(Σ), considering a primitive ideal I of ℓ1(Σ), the authors show that there exists a ∗-representation π of ℓ1(Σ) on Hilbert space such that the kernel is I, and that the closure in C∗(Σ) of an ideal of ℓ1(Σ) is an ideal of C∗(Σ).
A fixed point theorem for uniformly locally contractive mappings in a C-chainable cone rectangular metric space
2011
Recently, Azam, Arshad and Beg [ Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math. 2009] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result.
Locally Convex Quasi *-Algebras and their Representations
2020
This book is a review of the work the authors have done in the past 20 years on the theory of locally convex quasi *-algebras
MR2677289 Takakura, Mayumi Noncommutative integration in partial O∗-algebras. Fukuoka Univ. Sci. Rep. 40 (2010), no. 1, 1–20. (Reviewer: Francesco Ts…
2011
Operators in rigged Hilbert spaces: toward a spectral analysis
A note on semifinite von Neumann algebras
2009
In this note we give some techniques for constructing a faithful semi finite trace on a semifinite von Neumann algebra.
Slight extensions of positive linear functionals: two concrete realizations.
2009
In this paper we show, in full details, some example of slight extensions of a nonclosable positive linear functional ώ defined on a dense *-subalgebra Ao of a given topological *-algebra.
MR3299506 Reviewed Rădulescu, Florin(I-ROME2) On unbounded, non-trivial Hochschild cohomology in finite von Neumann algebras and higher order Berezin…
2015
If (At)t>1 is a family of finite von Neumann algebras with a Chapman-Kolmogorov set of linear maps (symbol system) (Φs,t), and if αt:A→A are isomorphisms in a finite family of von Neumann algebras, the corresponding Hochschild cocycles are related to an obstruction to the deformation of the set of linear maps (Φs,t) in the corresponding Chapman-Kolmogorov system (Φs,t)˜ of completely positive maps. In this set-up, the author introduces an invariant (c,Z) for a finite von Neumann algebra M, consisting of a 2-Hochschild cohomology cocycle c and a coboundary unbounded operator Z for c. With some assumptions on c and Z=α+X+iY (α>0, Y is antisymmetric), the existence of an unbounded derivation δ…
MR3257881 Reviewed Hadwin, Don Approximate double commutants in von Neumann algebras and C∗-algebras. Oper. Matrices 8 (2014), no. 3, 623–633. (Revie…
2015
In this paper, the author proves an asymptotic version of the double commutant theorem, in a particular set-up of commutative C∗ -algebras. More precisely, he considers the relative approximate double commutant of a C ∗-algebra with unit, and, using a theorem of characterization for a commutative C∗-subalgebra with unit (inspired by a well-known result due to Kadison for a von Neumann sub-algebra of type I), and from a theorem based on a Machado result, he proves that if A is a commutative C∗-subalgebra of a C∗-algebra B centrally prime with unit, then A is equal to its relative approximate double commutant. In the case where B is a von Neumann algebra, a distance formula is found.
Canonical Extensions of Conditional Probabilities and Compound Conditionals
2022
In this paper we show that the probability of conjunctions and disjunctions of conditionals in a recently introduced framework of Boolean algebras of conditionals are in full agreement with the corresponding operations of conditionals as defined in the approach developed by two of the authors to conditionals as three-valued objects, with betting-based semantics, and specified as suitable random quantities. We do this by first proving that the canonical extension of a full conditional probability on a finite algebra of events to the corresponding algebra of conditionals is compatible with taking subalgebras of events.