Search results for "C*-algebra"
showing 10 items of 67 documents
Codimensions of algebras and growth functions
2008
Abstract Let A be an algebra over a field F of characteristic zero and let c n ( A ) , n = 1 , 2 , … , be its sequence of codimensions. We prove that if c n ( A ) is exponentially bounded, its exponential growth can be any real number >1. This is achieved by constructing, for any real number α > 1 , an F-algebra A α such that lim n → ∞ c n ( A α ) n exists and equals α. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words.
A short note on O*-algebras and quantum dynamics
2009
We review some recent results concerning algebraic dynamics and O*-algebras. We also give a perturbative condition which can be used, in connection with previous results, to define a time evolution via a limiting procedure.
C*-seminorms generated by families of biweights on partial *-algebras
2011
If A[t] is a topological partial *-algebra with unit, topologized by the family of seminorms {p_a}, the notion of bounded element is defined, and some conditions to obtain an unbounded C*-seminorm q(x)=sup p_a(x) on A[t] with domain the subalgebra of bounded elements of A[t] are given.
Coordinate representation for non Hermitian position and momentum operators
2017
In this paper we undertake an analysis of the eigenstates of two non self-adjoint operators $\hat q$ and $\hat p$ similar, in a suitable sense, to the self-adjoint position and momentum operators $\hat q_0$ and $\hat p_0$ usually adopted in ordinary quantum mechanics. In particular we discuss conditions for these eigenstates to be {\em biorthogonal distributions}, and we discuss few of their properties. We illustrate our results with two examples, one in which the similarity map between the self-adjoint and the non self-adjoint is bounded, with bounded inverse, and the other in which this is not true. We also briefly propose an alternative strategy to deal with $\hat q$ and $\hat p$, based …
Locally convex quasi C*-algebras and noncommutative integration
2015
In this paper we continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm and we focus our attention on the so-called {\em locally convex quasi C*-algebras}. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra $(\X,\Ao)$, can be represented in a class of noncommutative local $L^2$-spaces.
Biweights on Partial *-Algebras
2000
This chapter is devoted to the systematic investigation of biweights on partial *-algebras. These are a generalization of invariant positive sesquilinear forms that still allows a Gel’fand—Naĭmark—Segal (GNS) construction of representations. In Section 9.1, we apply this GNS construction for biweights and we obtain *-representations and cyclic vector representations of partial *-algebras, and we give some examples of biweights. Section 9.2 is devoted to the investigation of the Radon—Nikodým theorem and the Lebesgue decomposition theorem for biweights on partial *-algebras. In Section 9.3, we define regular and singular biweights on partial *-algebras and we characterize them with help of t…
An overview on bounded elements in some partial algebraic structures
2015
The notion of bounded element is fundamental in the framework of the spectral theory. Before implanting a spectral theory in some algebraic or topological structure it is needed to establish which are its bounded elements. In this paper, we want to give an overview on bounded elements of some particular algebraic and topological structures, summarizing our most recent results on this matter.
Bounded elements in certain topological partial *-algebras
2011
We continue our study of topological partial *algebras, focusing our attention to the interplay between the various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between the strong and the weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *algebras, emphasizing the crucial role played by appropriate bounded elements, called $\M$-bounded. Finally, some remarks are made concerning representations in terms of the so-called partial GC*-algebras of operators.
Completely positive invariant conjugate-bilinear maps on partial *-algebras
2007
The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of commutative, locally convex quasi*-algebras are also discussed.
Banach partial *-algebras: an overview
2019
A Banach partial $*$-algebra is a locally convex partial $*$-algebra whose total space is a Banach space. A Banach partial $*$-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of these objects and display a number of examples, namely, $L^p$-like function spaces and spaces of operators on Hilbert scales or lattices. Finally we analyze the important cases of Banach quasi $*$-algebras and $CQ^*$-algebras.