A functional calculus for unbounded generalized scalar operators on Banach spaces

Dragoljub Kečkić and Ðorđe Krtinić

Vol. 249 (2011), No. 1, 135–156

DOI: 10.2140/pjm.2011.249.135

Abstract

We define weak and ultraweak functional calculus and construct using the Fourier transform technique an ultraweak functional calculus for an unbounded k-tuple of commuting generalized scalar operators T_j acting on a Banach space X. This functional calculus comprises the functions from the subset

of Sobolev space W_∞^α(ℝ), where α > 0. It also contains some unbounded functions. We also give examples and related results.

Keywords

functional calculus, Fourier transform, unbounded operators

Mathematical Subject Classification 2000

Primary: 46H25, 46H30, 47A60, 47L60

Secondary: 47L10, 47D06

Milestones

Received: 19 October 2009

Revised: 21 June 2010

Accepted: 25 June 2010

Published: 3 January 2011