Abstract

The partial isometries of [Formula: see text] form compact semigroups [Formula: see text]. We discuss here the liberation question for these semigroups, and for their discrete versions [Formula: see text]. Our main results concern the construction of half-liberations [Formula: see text] and of liberations [Formula: see text]. We include a detailed algebraic and probabilistic study of all these objects, justifying our “half-liberation” and “liberation” claims.

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