Solid extensions of the Cesàro operator on the Hardy space H2(D)

View/ Open
Date
2013-04-23MFO Scientific Program
Research in Pairs 2013Series
Oberwolfach Preprints;2013,11Author
Curbera, Guillermo P.
Ricker, Werner J.
Metadata
Show full item recordOWP-2013-11
Abstract
We introduce and study the largest Banach space of analytic functions on the unit disc which is solid for the coefficient-wise order and to which the classical Ces`aro operator $\mathcal{C}:H^2 \to H^2$ can be continuously extended, while still maintaining its values in $H^2$. Properties of this Banach space $\mathcal{H}(ces_2)$ are presented as well as a characterization of individual analytic functions which belong to $\mathcal{H}(ces_2)$. In addition, both the multiplier space of $\mathcal{H}(ces_2)$ and the spectrum of $\mathcal{C}:\mathcal{H}(ces_2) \to \mathcal{H}(ces_2)$ are determined.