Hermitian operators on $H^{\infty}_E$ and $S^{\infty}_{\mathcal{K}}$
Volume 130 / 2013
Colloquium Mathematicum 130 (2013), 51-59
MSC: 47B15, 47B38, 46E40.
DOI: 10.4064/cm130-1-5
Abstract
A complete characterization of bounded and unbounded norm hermitian operators on $H^{\infty}_E$ is given for the case when $E$ is a complex Banach space with trivial multiplier algebra. As a consequence, the bi-circular projections on $\displaystyle H^{\infty}_E$ are determined. We also characterize a subclass of hermitian operators on $S^{\infty}_{\mathcal{K}}$ for $\mathcal{K}$ a complex Hilbert space.
