Search results for "algebra"

CQ*-algebras and noncommutative measure

2012

In this paper we continue the investigations in [4], [5], [8], [13], [14], [15], and [19], of the structure of quasi *-algebras and extend the results in [1] and [2]. Here, noncommutative Tp-spaces are shown to constitute examples of a class of Banach C*-modules called CQ*-algebras. Moreover, it is shown that any (strongly) *-semisimple proper CQ*-algebra (X ,A), with A a separable C*-algebra, can be represented as a CQ*-algebra of type Tp.

Colombeau Algebras and convolutions generated by self-adjoint operators

2017

The role of convolution of functions in the construction of Colombeau algebras of generalized functions is analyzed, with particular referring to the commutative relation with the derivation operator. The possibility to consider the A-convolution, with A an unbounded self-adjoint operator in Hilbert space, is discussed. K

MR3377117 Reviewed Giordano, Paolo; Nigsch, Eduard A. Unifying order structures for Colombeau algebras. Math. Nachr. 288 (2015), no. 11-12, 1286–1302…

2015

Colombeau Algebras are differential algebras of generalized functions (that include the space of distributions) that are defined using a quotient set procedure involving particular classes of nets in a basic space E = (C∞(Ω))A, where Ω is an open subset of R n and A is an index set. The choice of such nets depends mainly on their asymptotic behavior over a suitable index set A. Many variants of Colombeau Algebras existing in the literature occur mainly due to different choices of the index set (and to the choice of asymptotic behavior). A purpose of this paper is to formally unify some of these algebras, redefining the asymptotic behavior on an abstract (pre-ordered) set of indices, and gen…

The completion of a C*-algebra with a locally convex topology

2006

There are examples of C*-algebras A that accept a locally convex *-topology t coarser than the given one, such that Ae[t] (the completion of A with respect to t) is a GB*-algebra. The multiplication of A[t] may be or not be jointly continuous. In the second case, Ae[t] may fail being a locally convex *-algebra, but it is a partial *-algebra. In both cases the structure and the representation theory of Ae[t] are investigated. If A[t+] denotes the t-closure of the positive cone A+ of the given C*-algebra A, then the property A[t]+ \cap (−A[t]+) = {0} is decisive for the existence of certain faithful *-representations of the corresponding *-algebra Ae[t].

Extension of representations in quasi *-algebras

2009

Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $\pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${\cal D} \subset {\cal H}$. Then we present several ways of extending $\pi^o$, by closure, to some larger quasi *-algebra contained in $A$, either by Hilbert space operators, or by sesquilinear forms on ${\cal D}$. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.

MR2544061 Ludkovsky, S. V. Algebras of operators in Banach spaces over the quaternion skew field and the octonion algebra. J. Math. Sci. (N. Y.) 144 …

2010

MR2905225 Rowe, Stephen; Fang, Junsheng; Larson, David R. P1 subalgebras of Mn(C). Involve 4 (2011), no. 3, 213–250. (Reviewer: Camillo Trapani)

2012

A note on partial*–algebras and spaces of distributions

2014

Given a rigged Hilbert space (D,H,D'), the spaces D_{loc are considered. It is shown that, if D is a Hilbert *-algebra, D_{loc} carry out a natural structure of partial *-algebra. Furthermore, on D_{loc} it is defined a topology, so that D_{loc} is an interspace. Examples from distributions theory are considered.

Perturbations of polaroid type operators on Banach spaces and Applications

2011

We study the permanence of polaroid type conditions under perturbations

Faithfully representable topological *-algebras: some spectral properties

2018

A faithfully representable topological *-algebra (fr*-algebra) A0 is characterized by the fact that it possesses sufficiently many *-representations. Some spectral properties are examined, by constructing a convenient quasi *-algebra A over A0, starting from the order bounded elements of A0.