Similarity of quasinilpotent operators and Norm estimates on Hardy spaces with interpolation of applications to controllability

Abstract

We Show the uniqueness of the norm on the Lebesgue space of the compact group. We give some applications of the property of Kazhdan to the method of automatic continuity. We determine the similarity of quasinilpotent operators. The symmetric Meixner- Pollaczek polynomials and a system of orthogonal polynomials with Hardy spaces for the strip are considered. We investigate the behaviour of the Lebesgue space of the integral means of the analytic functions and the vector- valued BMOA and multipliers. We determine the norm estimates for operators from the Hardy space to the Hilbert space and the interpolation by the vector- valued analytic function that have applications to controllability. We discuss and show new abstract Hardy spaces.