Related papers: On representations of partial ^*-algebras based on…
In this paper we study the bicomplex version of weighted Hardy spaces. Further, we describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we generalize some results which holds for the classical weighted Hardy…
A well-known result going back to the 1930s states that all bounded linear operators mapping scalar-valued $L^1$-spaces into $L^\infty$-spaces are kernel operators and that in fact this relation induces an isometric isomorphism between the…
The induction and reduction precesses of an O*-vector space $\M$ obtained by means of a projection taken, respectively, in $\M$ itself or in its weak bounded commutant $\M'_\w$ are studied. In the case where $\M$ is a partial GW*-algebra,…
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…
Abstract. We generalize the $b$-ary binomial coefficients with negative entries, which is based on the generating function obtained in early work. Besides an explicit expression involving the restricted partition, several properties such as…
Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to assure the existence of enveloping actions. This allows…
An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…
The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: the first one takes into account the inductive structure provided by certain families of…
These notes cover the contents of three survey lectures held at the ICTP Trieste Summer school on High dimensional manifold theory 2001. They introduce techniques coming from the theory of operator algebras. We will focus on the basic…
The behaviour of the generalized Hilbert operator associated with a positive finite Borel measure $\mu$ on $[0,1)$ is investigated when it acts on weighted Banach spaces of holomorphic functions on the unit disc defined by sup-norms and on…
The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic…
We introduce Banach algebras associated to twisted \'etale groupoids $(\mathcal{G},\mathcal{L})$ and to twisted inverse semigroup actions. This provides a unifying framework for numerous recent papers on $L^p$-operator algebras and the…
In this paper we develop a method of constructing Hilbert spaces and the representation of the formal algebra of quantum observables in deformation quantization which is an analog of the well-known GNS construction for complex…
The observation that $n$ pairs of para-Bose (pB) operators generate the universal enveloping algebra of the orthosymplectic Lie superalgebra $osp(1/2n)$ is used in order to define deformed pB operators. It is shown that these operators are…
Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…
We consider positive semidefinite kernels which have values given by bounded linear operators on certain bundles of Hilbert spaces and which are invariant under actions of $*$-semigroupoids. For these kernels, we prove that there exist…
The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^*$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on…
A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semi-bounded if the corresponding operators $i\dd\pi(x)$ from the derived representations are uniformly bounded from above on some non-empty open subset…
We study the space of irreducible representations of a crossed product C*-algebra AxG, where G is a finite group. We construct a space $\Gamma$ which consists of pairs of irreducible representations of A and irreducible projective…
Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for…