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BY 4.0 license Open Access Published by De Gruyter Open Access December 31, 2019

The Blum-Hanson Property

  • Sophie Grivaux EMAIL logo
From the journal Concrete Operators


Given a (real or complex, separable) Banach space, and a contraction T on X, we say that T has the Blum-Hanson property if whenever x, yX are such that Tnx tends weakly to y in X as n tends to infinity, the means


tend to y in norm for every strictly increasing sequence (nk) k≥1 of integers. The space X itself has the Blum-Hanson property if every contraction on X has the Blum-Hanson property. We explain the ergodic-theoretic motivation for the Blum-Hanson property, prove that Hilbert spaces have the Blum-Hanson property, and then present a recent criterion of a geometric flavor, due to Lefèvre-Matheron-Primot, which allows to retrieve essentially all the known examples of spaces with the Blum-Hanson property. Lastly, following Lefèvre-Matheron, we characterize the compact metric spaces K such that the space C(K) has the Blum-Hanson property.

MSC 2010: 47A35


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Received: 2019-10-16
Accepted: 2019-12-09
Published Online: 2019-12-31

© 2019 Sophie Grivaux, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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