相关论文: Orthogonal Pure States in Operator Theory

In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…

multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…

We introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…

We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to…

We construct a topology on the standard Hilbert module $l^2(\mathcal A)$ over a unital $W^*$-algebra $\mathcal A$ such that any "compact" operator, (i.e.\ any operator in the norm closure of the linear span of the operators of the form…

We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact…

We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…

With the aim of constructing coherent states for many-body systems consisting of six kinds of boson operators, a possible form of the orthogonal set is presented in terms of monomial with respect to state generating operators. In connection…

We investigate some new classes of operator algebras which we call semi-$\sigma$-finite subdiagonal and Riesz approximable. These constitute the most general setting to date for a noncommutative Hardy space theory based on Arveson's…

Several mathematicians, including myself, have studied some unifications in general topological spaces as well as in fuzzy topological spaces. For instance in our earlier works, using operations on topological spaces, we have tried to unify…

The definition of 'classical state', and how it was used in earlier work to prove a decomposition theorem internally in the language of State Property Systems, presupposes as an additional datum an orthocomplementation on the property…

In this article, we study the properties of the autonomous superposition operator on the space of formal power series, including those with nonzero constant term. We prove its continuity and smoothness with respect to the topology of…

An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…

For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive,…

We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in…

In this article we classify additive operations in connective K-theory with various torsion-free coefficients. We discover that the answer for the integral case requires understanding of the $\hat{{\mathbb{Z}}}$ one. Moreover, although…

This paper introduces a novel topology, referred to as the star topology, on finite graphs. By treating vertices and edges as points in a unified space, we explore continuous maps between Bare representations of a graph and their…

A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all…