Abstract.
Let X be any Banach space and T a bounded operator on X. An extension 
of the pair (X,T) consists of a Banach space 
in which X embeds isometrically through an isometry i and a bounded operator
on such that 
When X is separable, it is additionally required that be separable. We say that is a topologically transitive extension of (X, T) when is topologically transitive on , i.e. for every pair 
of non-empty open subsets of there exists an integer n such that 
is non-empty. We show that any such pair (X,T) admits a topologically transitive extension , and that when H is a Hilbert space, (H,T) admits a topologically transitive extension 
where 
is also a Hilbert space. We show that these extensions are indeed chaotic.
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Mathematics Subject Classification (2000): 47 A 16
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Grivaux, S. Topologically transitive extensions of bounded operators. Math. Z. 249, 85–96 (2005). https://doi.org/10.1007/s00209-004-0690-8
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DOI: https://doi.org/10.1007/s00209-004-0690-8