Search

We obtain operator-valued analogues of Bohr's inequality involving both the absolute values of operators and their norms, that when restricted to the scalar case imply the classical Bohr inequality. In the scalar case we extend Bohr's inequality to the case where one function is majorized by another function, to the Hardy space, $H^2(\mathbb{D})$, and to bounded analytic functions on the annulus.

We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting $n$-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal $2$-variable weighted shifts, we then find the precise relation between the Berger measure of the pair and the Berger measures of the shifts associated to horizontal rows and vertical columns of weights.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

EXTENSIONS OF BOHR'S INEQUALITY

DISINTEGRATION-OF-MEASURE TECHNIQUES FOR COMMUTING MULTIVARIABLE WEIGHTED SHIFTS

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

EXTENSIONS OF BOHR'S INEQUALITY

DISINTEGRATION-OF-MEASURE TECHNIQUES FOR COMMUTING MULTIVARIABLE WEIGHTED SHIFTS