Related papers: Characterizations of Ordered Self-adjoint Operator…
We generalize an important class of Banach spaces, namely the $M$-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided $M$-embedded operator spaces are the operator spaces which are one-sided $M$-ideals…
In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute…
Motivated by a random matrix theory model from wireless communications, we define random operator-valued matrices as the elements of $L^{\infty-}(\Omega,{\mathcal F},{\mathbb P}) \otimes M_d({\mathcal A})$ where $(\Omega,{\mathcal…
We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…
We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential…
We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension $d$ if and only if there exists a $d^2$-dimensional operator system satisfying certain order-theoretic conditions. We also…
Ordered locally convex spaces is an important classes of spaces in the theory of ordered topological vector spaces just as locally convex spaces in the theory of topological vector spaces. Some special classes of ordered locally convex…
We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family,…
Global invertible symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to non-invertible symmetries by considering unitary actions of higher fusion category…
In this paper we {\em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be…
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
Weyl-von Neumann Theorem asserts that two bounded self-adjoint operators $A,B$ on a Hilbert space $H$ are unitarily equivalent modulo compacts, i.e., $uAu^*+K=B$ for some unitary $u\in \mathcal{U}(H)$ and compact self-adjoint operator $K$,…
We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…
We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary…
A vector space S of linear operators between finite-dimensional vector spaces U and V is called locally linearly dependent (in abbreviate form: LLD) when every vector x in U is annihilated by a non-zero operator in S. By a duality argument,…
This paper charts a very direct path between the categorical approach to quantum mechanics, due to Abramsky and Coecke, and the older convex-operational approach based on ordered vector spaces (recently reincarnated as "generalized…
We study finitely cyclic self-adjoint operators in a Hilbert space, i.e. self-adjoint operators that posses such a finite subset in the domain that the orbits of all its elements with respect to the operator are linearly dense in the space.…
The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the…
Orthonormal systems in commutative $L_2$ spaces can be used to classify Banach spaces. When the system is complete and satisfies certain norm condition the unconditionality with respect to the system characterizes Hilbert spaces. As a…
Unitary operations are physically implementable. We further the understanding of such operations by studying the possible forms of nonlocal unitary operators, which are bipartite or multipartite unitary operators that are not tensor product…