Related papers: Real structure in operator spaces, injective envel…

This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…

A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…

In this paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with "complex Poincar\'e group" ISO(4,C).

In this article we give a short and informal overview of some aspects of the theory of C*- and von Neumann algebras. We also mention some classical results and applications of these families of operator algebras.

Let $\mathfrak{g}$ be a compact simple Lie algebra. We modify the quantized enveloping $^*$-algebra associated to $\mathfrak{g}$ by a real-valued character on the positive part of the root lattice. We study the ensuing Verma module theory,…

In this article, we describe how coalgebraic structures on operads induce algebraic structures on their categories of algebras and coalgebras.

We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…

Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let $G$ be a complex reductive group, let $V$ be a $G$-module, and let $v,w$ be elements of $V$. Determine if $w$…

We give an operator space characterization of subalgebras of $C(\Omega,M_n)$. We also describe injective subspaces of $C(\Omega,M_n)$ and then give applications to sub-TROs of $C(\Omega,M_n)$. Finally, we prove an `$n$-minimal version' of…

We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…

In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.

The set of effect operators in a complex Hilbert space can be injectively embedded into the set of functions from the set of one-dimensional projections to the real interval [0,1]. Properties of this injection are investigated.

We provide a construction of Roe (C*-)algebras of general coarse spaces in terms of coarse geometric modules. This extends the classical theory of Roe algebras of metric spaces and gives a unified framework to deal with either uniform or…

This paper mainly concerns the von Neumann algebras induced by a tuple of multiplication operators on Bergman spaces which arise essentially from holomorphic proper maps over higher dimensional domains. We study the structures and abelian…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

We explore a wider theoretical framework that has quantum field theory built-in, taking the fact that quantum mechanics is reconstructed from quantum field theory as a hint. We formulate a quantum theory with an embedded structure by…

We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…

In this note devoted to some aspects of the inverse problem of representation theory the attention is concentrated on the interrelations between various algebraic structures (algebras with operators) unraveled by different solutions of the…

We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic…

In this article, we define operator algebras internal to a rigid C*-tensor category $\mathcal{C}$. A C*/W*-algebra object in $\mathcal{C}$ is an algebra object $\mathbf{A}$ in $\operatorname{ind}$-$\mathcal{C}$ whose category of free…