Hermitian operators on $H^{\infty}_E$ and $S^{\infty}_{\mathcal{K}}$

Tom 130 / 2013

James Jamison Colloquium Mathematicum 130 (2013), 51-59 MSC: 47B15, 47B38, 46E40. DOI: 10.4064/cm130-1-5


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.


  • James JamisonDepartment of Mathematical Sciences
    The University of Memphis
    Memphis, TN 38152, U.S.A

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