Abstract of a paper by Marius Junge, Zhong-Jin Ruan and David Sherman
This is an announcement for the paper "A classification for 2-isometries of noncommutative Lp-spaces" by Marius Junge, Zhong-Jin Ruan and David Sherman. Abstract: 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. Archive classification: Operator Algebras Remarks: 25 pages The source file(s), 2isom.tex: 88005 bytes, is(are) stored in gzipped form as 0402181.gz with size 26kb. The corresponding postcript file has gzipped size 111kb. Submitted from: dasherma@ux1.cso.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.OA/0402181 or http://arXiv.org/abs/math.OA/0402181 or by email in unzipped form by transmitting an empty message with subject line uget 0402181 or in gzipped form by using subject line get 0402181 to: math@arXiv.org.
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Dale Alspach