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International Journal of Functional Analysis, Operator Theory and Applications

International Journal of Functional Analysis, Operator Theory and Applications
Volume 10, Issue 2, Pages 95 - 120 (June 2018)
http://dx.doi.org/10.17654/FA010020095

CHARACTERIZATIONS OF THE SERIES GROUP GENERATORS ON HILBERT SPACES AND THE -CALCULUS

Simon Joseph, Manal Juma and Mohamed Mustafa

Abstract:

We give necessary and sufficient conditions for the sequence of operators on a Hilbert space to have a bounded -calculus on a vertical strip symmetric to the imaginary axis. From this, a characterization of group generators on Hilbert spaces is obtained yielding recent results of Liu and Zwart as corollaries by Haase [9].