论文信息 - A mean ergodic theorem for resolvent operators

A mean ergodic theorem for resolvent operators

AbstractLet {R(t)}t≥0 be a uniformly bounded strongly continuous resolvent operator for the Volterra equation of convolution typeu=g+k*Au, whereA is a closed and densely defined operator on a Banach spaceX andk is a scalar kernel. We show that $$\overline {Ran\left( A \right)} \oplus Ker\left( A \right) = X$$ whenX is reflexive and that the average given by {R(t)}t≥0 andk converges on the closed subspace $$X_k = \overline {Ran\left( A \right)} \oplus Ker\left( A \right)$$ to a bounded projection.

Carlos Lizama | C. Lizama

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