Hahn-Banach type theorems for adjoint semigroups.
On the topology induced by the adjoint of a semigroup of operators.
Individual stability of Co-semigroups with uniformly bounded local resolvent.
Abstract multiplication semigroups.
On the orbits of an operator with spectral radius one
Continuity versus nonexistence for a class of linear stochastic Cauchy problems driven by a Brownian motion
Let denote the generator of the rotation group in the space , where denotes the unit circle. We show that the stochastic Cauchy problem where is a standard Brownian motion and is fixed, has a weak solution if and only if the stochastic convolution process has a continuous modification, and that in this situation the weak solution has a continuous modification. In combination with a recent result of Brzeźniak, Peszat and Zabczyk it follows that (1) fails to have a weak solution for all...
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