Functional Spectrum of Contractions With InEqualties for Commutators and Sharp Remainder Estimates in Weyl Formula

Abstract

We show the Berger – show Theorem and operator theory in the Hardy module space over the Bidisc. Inner sequences based invariant subspaces in the Hardy space are also considered. We study some operator sand norm inequalities concerning generalized inverses. We show the Weyl asymptotic formula for the Laplacian on certain domains with values boundaries and sharp remainder estimates in the Weyl formula for the Newmann Laplacian on a class of planar regions. We discussed the functional spectrum of contraction. We investigate some norm inequalities for certain operator sums and differences of positive operator. We also established norm inequalities for finite sums and inequalities for commutators of positive operators.