Related papers: Cancellability and Regularity of Operator Connecti…
A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the joint-continuity from above. A mean is a normalized connection. In this paper, we show that there is a one-to-one…
An operator mean is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above, the transformer inequality and the fixed-point property. It is well known that there are one-to-one…
An axiomatic theory of operator connections and operator means was investigated by Kubo and Ando in 1980. A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the…
A connection in Kubo-Ando sense is a binary operation for positive operators on a Hilbert space satisfying the monotonicity, the transformer inequality and the continuity from above. A mean is a connection $\sigma$ such that $A \sigma A =A$…
In this paper, we show that there is a one-to-one correspondence between operator monotone functions on the nonnegative reals and finite Borel measures on the unit interval. This correspondence appears as an integral representation of…
We propose a notion of operator monotonicity for functions of several variables, which extends the well known notion of operator monotonicity for functions of only one variable. The notion is chosen such that a fundamental relationship…
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…
We consider a number operator-annihilation operator uncertainty as a well behaved alternative to the number-phase uncertainty relation, and examine its properties. We find a formulation in which the bound on the product of uncertainties…
Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal…
We prove that for elliptic and canceling linear differential operators $\mathbb{B}$ of order $n$ on $\mathbb{R}^n$, continuity of a map $u$ can be inferred from the fact that $\mathbb{B} u$ is a measure. We also prove strict continuity of…
The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand…
The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between finite-dimensional and infinite-dimensional spaces. We first…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…
We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
We consider all 16 unary operations that, given a homogeneous binary relation R, define a new one by a boolean combination of xRy and yRx. Operations can be composed, and connected by pointwise-defined logical junctors. We consider the…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…