Multipliers and operator algebras on bounded analytic functions

Multipliers and Dual Operator Algebras

In a previous paper we showed how the main theorems characterizing operator algebras and operator modules, fit neatly into the framework of the ‘noncommutative Shilov boundary’, and more particularly via the left multiplier operator algebra of an operator space. As well as giving new characterization theorems, the approach of that paper allowed many of the hypotheses of the earlier theorems to ...

On Bounded Analytic Functions

The objective of this paper is to give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [l] and Garabedian [2].1 While it is admitted that the main idea to be used is more in the nature of a lucky guess than of a method, it will be found that the gain in brevity and simplicity of the argument is considerable. As a by-product, we shall also obtain a...

Multipliers on Spaces of Analytic Functions

In the paper we find, for certain values of the parameters, the spaces of multipliers ( H(p, q, α), H(s, t, β) ) and ( H(p, q, α), ls ) , where H(p, q, α) denotes the space of analytic functions on the unit disc such that (1 − r)Mp(f, r) ∈ Lq( dr 1−r ). As corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces. §0. Introduction. Given two sequence spaces X ...

FUNCTIONS ON MULTIPLIERS OF p-FOURIER ALGEBRAS

Operator Algebras for Analytic Varieties

We study the isomorphism problem for the multiplier algebras of irreducible complete Pick kernels. These are precisely the restrictionsMV of the multiplier algebraM of Drury-Arveson space to a holomorphic subvariety V of the unit ball. We find thatMV is completely isometrically isomorphic toMW if and only if W is the image of V under a biholomorphic automorphism of the ball. In this case, the i...