Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591872 | Journal of Functional Analysis | 2009 | 21 Pages |
Abstract
There is a standard notion of type for a sectorial linear operator acting in a Banach space. We introduce a notion of asymptotic type for a linear operator V, involving estimates on the resolvent −1(λI+V) as λ→0. We show, for example, that if V is sectorial and of asymptotic type ω then the fractional power Vα is of asymptotic type αω for a suitable range of positive α. Moreover, we establish various properties of the operator ; in particular, this operator is of asymptotic type 0, for a sectorial operator V. This result has an application to the construction of operators satisfying the well-known Ritt resolvent condition.
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