Operators with smooth functional calculi

Details Operators with smooth functional calculi Operators with smooth functional calculi

2005-03-14

arxiv.org/abs/math/0503256v1

Mathematics

Spectral Theory

Scientific paper

We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings. Moreover, the class is closed under tensor product of commuting operators. In general an operator in this class has no resolvent in the usual sense so the spectrum must be defined in terms of the functional calculus. We also consider invariant subspaces and spectral decompositions.

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