Is it correct to say: for any family of bounded operators (proper subset of B(H)) acting on a non-separable Hilbert space there is a non-trivial subspace of the Hilbert space that reduces the family? I know that this is true for any operator on the space so, I assume that it holds also for the von Neumann algebra generated by this operator. Can we generalize to non-commutative families? If the answers is positive (or positive with certain restriction imposed on the family) how can we show it? Is there any reference?
2026-04-17 11:05:30.1776423930
Reducible families of bounded operators on non-separable Hilbert spaces
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