K. V. Storozhuk

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math.FA2010

Obstructions for uniform stability of C_0-semigroup

K. V. Storozhuk

Let T be a C_0-semigroup on X with generator A. We prove that if the abscissa of uniform boundedness of the resolvent A is non-negative then for each a non-decreasing function h:[0…

math.FA2010

Slowly Changing Vectors and the Asymptotic Finite-Dimensionality of an Operator Semigroup

K. V. Storozhuk

Let $T : X \to X$ be a linear power bounded operator on Banach space. Let $X_{0}$ is a subspace of vectors tending to zero under iterating of $T$ . We prove that if $X_{0}$ is not equal to…