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Unitary Brownian motions are linearizable

Boris Tsirelson
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Abstract

Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent one-dimensional Brownian motions. The proof involves continuous tensor products and continuous quantum measurements. A by-product: a Brownian motion in a separable F-space (not locally convex) is a Gaussian process.

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Boris Tsirelson. 1998-06-19. Unitary Brownian motions are linearizable. https://arxiv.org/abs/math/9806112

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