Journal of Operator Theory

Volume 48, Issue 2, Fall 2002 pp. 385-418.

Spectral properties and norm estimates associated to the $C_{\rm c}^{(k)}$-functional calculus

Authors: Jose E. Gale (1), Pedro J. Miana (2), and Tadeusz Pytlik (3)
Author institution: (1) Departamento de Matematicas, Universidad de Zaragoza, 50009 Zaragoza, Spain
(2) Departamento de Matematicas, Universidad de Zaragoza, 50009 Zaragoza, Spain
(3) Instytut Matematyczny, Uniwersytet Wroclawski, 50384 Wroclaw, Poland

Summary: We show that the Davies functional calculus and the $AC^{(\nu)}$-calculus coincide under common hypotheses. Then we apply the calcul us to operators on Banach spaces, to investigate spectral invariance and norm estimates linked to abstract Cauchy equations. This extends some previous results in the area, and unifies diverse approaches. The theory is applied to op erators related to multiplier theory on Lie groups.

Keywords: Functional calculus, holomorphic semigroups, abstract Cauchy problem, multipliers

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