Abstract
Notions of weak and uniformly weak mixing (to zero) are defined for bounded sequences in arbitrary Banach spaces. Uniformly weak mixing for vector sequences is characterized by mean ergodic convergence properties. This characterization turns out to be useful in the study of multiple recurrence, where mixing properties of vector sequences, which are not orbits of linear operators, are investigated. For bounded sequences, which satisfy a certain domination condition, it is shown that weak mixing to zero is equivalent with uniformly weak mixing to zero.
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Dedicated to the memory of our colleague Gert K. Pedersen
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Zsidó, L. (2006). Weak Mixing Properties of Vector Sequences. In: Dritschel, M.A. (eds) The Extended Field of Operator Theory. Operator Theory: Advances and Applications, vol 171. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7980-3_17
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DOI: https://doi.org/10.1007/978-3-7643-7980-3_17
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