The Kitai criterion and backward shifts

Shkarin, Stanislav

doi:10.1090/S0002-9939-08-09179-X

The Kitai criterion and backward shifts
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Proc. Amer. Math. Soc. 136 (2008), 1659-1670 Request permission

Abstract:

It is proved that for any separable infinite dimensional Banach space $X$, there is a bounded linear operator $T$ on $X$ such that $T$ satisfies the Kitai criterion. The proof is based on a quasisimilarity argument and on showing that $I+T$ satisfies the Kitai criterion for certain backward weighted shifts $T$.

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