Related papers: A General Verification for Functional Completeness…
We generalize a preceding simple proof of the Jamiolkowski criterion to check whether a given linear map between algebras of operators is completely positive or not. The generalization is performed to embrace all algebras of Hilbert-Schmidt…
This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…
Commutativity of data structure methods is of ongoing interest, with roots in the database community. In recent years commutativity has been shown to be a key ingredient to enabling multicore concurrency in contexts such as parallelizing…
This paper is concerned with universality properties of composition operators $C_f$, where the symbol $f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of $C_f$ when $f$ is…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
It is proved recently by Benamara-Nikolski that a contraction having finite defects and spectrum not filling in the closed unit disc, is similar to a normal operator if and only if it has the so-called linear resolvent growth property. We…
Formally verified compilers and formally verified static analyzers are a solution to the problem that certain industries face when they have to demonstrate to authorities that the object code they run truly corresponds to its source code…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
This paper presents a formalized analysis of the sigmoid function and a fully mechanized proof of the Universal Approximation Theorem (UAT) in Isabelle/HOL, a higher-order logic theorem prover. The sigmoid function plays a fundamental role…
In this thesis a comprehensive verification framework is proposed to contend with some important issues in composability verification and a verification process is suggested to verify composability of different kinds of systems models, such…
A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…
In the paper, we revisit several approaches to the concept of uniform completion $X^{\mathrm{ru}}$ of a vector lattice $X$. We show that many of these approaches yield the same result. In particular, if $X$ is a sublattice of a uniformly…
In this paper we introduce and study absolute continuity and singularity of positive operators acting on anti-dual pairs. We establish a general theorem that can be considered as a common generalization of various earlier Lebesgue-type…
Program safety (i.e., absence of undefined behaviors) is critical for correct operation of computer systems. It is usually verified at the source level (e.g., by separation logics) and preserved to the target by verified compilers (e.g.,…
In this paper we initiate the study of real operator monotonicity for functions of tuples of operators, which are multivariate structured maps with a functional calculus called free functions that preserve the order between real parts (or…
We develop a general theory of operator realizations, or ``linear representations" of analytic functions in several non-commuting variables about a matrix-centre. In particular we show that a non-commutative function has a matrix-centre…
By investigating which level of universality composition operators $C_f$ can have, where the symbol $f$ is given by the restriction of a transcendental entire function to suitable parts of the Fatou set of $f$, this work combines the theory…
Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…
Abstract. In this work we derive a sufficient condition to ensure certain genus 0 entire function that can have only negative zeros. We also apply this result to the Riemann hypothesis and generalized Riemann hypothesis for some primitive…
Local Completeness Logic (LCL) has been put forward as a program logic for proving both the correctness and incorrectness of program specifications. LCL is an abstract logic, parameterized by an abstract domain that allows combining over-…