In this article we study the properties of the hyperinterpolation operator on the unit disk D in R. We show how the hyperinterpolation can be used in connection with the Kumar-Sloan method to approximate the solution of a nonlinear Poisson equation on the unit disk (discrete Galerkin method). A bound for the norm of the hyperinterpolation operator in the space C(D) is derived. Our results prove...

Some Lipschitz norm and BMO norm inequalities for potential operator to the versions of differential forms are obtained, and some properties of a new kind of A λ3 r λ 1 , λ 2 , ΩΩ weight are derived.

In this work, the gap between operator norm and spectral radius for square of antidiagonal block matrices in direct sum Banach spaces has been investigated, also numerical same Hilbert studied.

We show a continuity theorem for Stinespring’s dilation: two completely positive maps between arbitrary C∗-algebras are close in cb-norm iff we can find corresponding dilations that are close in operator norm. The proof establishes the equivalence of the cb-norm distance and the Bures distance for completely positive maps. We briefly discuss applications to quantum information theory.

In \cite{Tre_PSI20} we introduce the concept of a $\mu$-norm for bounded operator in Hilbert space. The main motivation is extension measure entropy to case quantum systems. this paper recall basic results from and present further on $\mu$-norm. More precisely, specify three classes unitary operators which generates bistochastic operator. We plan use latter construction entropy.