Related papers: Ordered C*-modules
Let $V$ be a vertex operator algebra and $g$ an automorphism of $V$ of finite order $T$. For any $m, n \in(1/T) \mathbb N$, an $A_{g,n}(V)\!-\!A_{g,m}(V)$ bimodule $A_{g,n, m}(V)=V/O_{g,n,m}(V)$ was defined by Dong and Jiang, where…
Wakimoto modules are representations of affine Kac-Moody algebras in Fock modules over infinite-dimensional Heisenberg algebras. In these lectures we present the construction of the Wakimoto modules from the point of view of the vertex…
We introduce a construction that associates, to each finite dimensional k-vector space V, a family of projective k-varieties that comes equipped with the structure of a operad in the category of k-schemes. When dim V = 1, this operad…
In this paper, we use the twisted regular representation theory of vertex operator algebras to construct bimodules over twisted Zhu algebras, extending Haisheng Li's work in untwisted scenarios. Moreover, a conjecture of Dong and Jiang on…
Utilizing the Birkhoff--James orthogonality, we present some characterizations of the norm-parallelism for elements of $\mathbb{B}(\mathscr{H})$ defined on a finite dimensional Hilbert space, elements of a Hilbert $C^*$-module over the…
Introduced by Duffin and Schaefer as a part of their work on nonhamonic fourrier series in 1952, the theory of frames has undergone a very interesting evolution in recent decades following the multiplicity of work carried out in this field.…
Let $Z \subset \mathbb{A}^k$ be an affine scheme over $\C$ and $\J Z$ its jet scheme. It is well-known that $\mathbb{C}[\J Z]$, the coordinate ring of $\J Z$, has the structure of a commutative vertex algebra. This paper develops the…
Certain $*$-semigroups are associated with the universal $C^*$-algebra generated by a partial isometry, which is itself the universal $C^*$-algebra of a $*$-semigroup. A fundamental role for a $*$-structure on a semigroup is emphasized, and…
In this paper we introduce a generalization of Hilbert C-modules which are pre- Finsler module namely C-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will…
We construct the Calderon projection on the space of Cauchy datas for a twisted Dirac operator in the Mischenko--Fomenko pseudodifferential calculus for operators acting on bundles of finitely generated $C^*$--Hilbert modules on a compact…
Given a Hilbert module E over a C*-algebra A, we show that the collection of all bounded A-module operators acting on E forms the reflexive closure for the algebra of the adjointable operators. We also make an observation regarding the…
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…
We develop a tensor categorical duality in the sprit of the Tannaka-Krein duality for the C*-algebras admitting the Yetter-Drinfeld module structure over a compact quantum group. Under this duality, given a reduced compact quantum group G,…
This paper explores idempotent and nilpotent operators in bicomplex spaces, focusing on their properties and behavior. We define idempotent and nilpotent matrices in this framework and derive related results. Several theorems are presented…
The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$ on a Hilbert…
We construct projective limit of projective sequence in the following categories: Archimedean order unit spaces with unital positive maps and operator systems with unital completely positive maps. We prove that inductive limit and…
Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…
We study completely positive module maps on $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions. We extend several well known dilation and extension results to this setup, including the Stinespring…
We use a result of Barron, Dong and Mason to give a natural isomorphism between the category of twisted modules and the category of quasi-modules of a certain type for a general vertex operator algebra.
We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…