A classification for 2-isometries of noncommutative Lp-spaces

Details A classification for 2-isometries of noncommutative Lp-spaces A classification for 2-isometries of noncommutative Lp-spaces

2004-02-11

arxiv.org/abs/math/0402181v1

Mathematics

Operator Algebras

25 pages

Scientific paper

In this paper we extend previous results of Banach, Lamperti and Yeadon on isometries of Lp-spaces to the non-tracial case first introduced by Haagerup. Specifically, we use operator space techniques and an extrapolation argument to prove that every 2-isometry T : Lp(M) to Lp(N) between arbitrary noncommutative Lp-spaces can always be written in the form T(phi^{1/p}) = w (phi circ pi^{-1} circ E)^{1/p}, for phi in M_*^+. Here pi is a normal *-isomorphism from M onto the von Neumann subalgebra pi(M) of N, w is a partial isometry in N, and E is a normal conditional expectation from N onto pi(M). As a consequence of this, any 2-isometry is automatically a complete isometry and has completely contractively complemented range.

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