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A general setup is provided for theorems of the Blum-Hanson type. Notions of strongly and weakly mixing sequences of elements in a Hubert space are defined, and equivalent characterizations are derived. It turns out that many known generalizations of the Blum-Hanson theorem are special cases of an abstract version which is also suitable for the nonlinear situation.doi:10.2307/2045691 fatcat:yqjr4xa6rjb6rfaq423jnc7yre