Contractive projections and operator spaces |
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| Authors: | Matthew Neal Bernard Russo |
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| Affiliation: | Department of Mathematics, Denison University, Granville, Ohio 43023 ; Department of Mathematics, University of California, Irvine, California 92697-3875 |
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| Abstract: | Parallel to the study of finite-dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces  ,  , generalizing the row and column Hilbert spaces  and  , and we show that an atomic subspace  that is the range of a contractive projection on  is isometrically completely contractive to an  -sum of the  and Cartan factors of types 1 to 4. In particular, for finite-dimensional  , this answers a question posed by Oikhberg and Rosenthal. Explicit in the proof is a classification up to complete isometry of atomic w -closed  -triples without an infinite-dimensional rank 1 w -closed ideal. |
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| Keywords: | Contractive projection operator space complete contraction Cartan factor injective mixed-injective $JC^*$-triple $JW^*$-triple ternary algebra |
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