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Conditions for uniqueness of fractional powers
(Maltepe Üniversitesi, 2009) Pastor, Javier
It is well-known the important role that plays, in relation to Cauchy problems associated to an operator A, the fact that A has an additive family of closed operators {At}t>0, A1 ? A, such that the operator ?At is the generator of a semigroup of bounded linear operators for small exponents t. The need of considering the inverse, the closure or the adjoint of single-valued linear operator leads in a natural way to deal with multivalued linear operator. Applications of multivalued methods to degenerated evolution equations can be found in [1]. A theory of fractional powers for nonnegative multivalued linear operators in a complex Banach space was introduced in [4]. This work is devoted to the study of uniqueness of a continuous semigroup of fractional powers for a nonnegative multivalued linear operator A. In [3] we can find several uniqueness results in the single-valued case. Very recently, in [1], it has been established a uniqueness result analogous to the presented here, but only for injective single-valued and nonnegative linear operators.