We prove that a composition operator is bounded on the Hardy space H of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative λ there. In this case the norm, essential norm, and spectral radius of the operator are all equal to √ λ.

for an n-by-n complex matrix a in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of a. in this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...

The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of twoand three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization...

Abstract Let ???? be a complex Hilbert space and A non-zero positive bounded linear operator on . The main aim of this paper is to discuss general method develop -operator seminorm -numerical radius inequalities semi-Hilbertian operators using the existing corresponding Among many other we prove that if S , T X ? ???? ( ), i.e., -adjoint exist, then <m:math xmlns:m="http://www.w3.org/1998/Math/...

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

Abstract. By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently...

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.