A Maurey type result for operator spaces |
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Authors: | Marius Junge |
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Affiliation: | a Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall 1409 W. Green Street, Urbana, IL 61801, USA b Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1 |
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Abstract: | The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C(K) and ?2 is 2-summing. However, it is shown in [M. Junge, Embedding of the operator space OH and the logarithmic ‘little Grothendieck inequality’, Invent. Math. 161 (2) (2005) 225-286] that the operator space analogue fails. Not every cb-map is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem: every cb-map is (q,cb)-summing for any q>2 and hence admits a factorization ‖v(x)‖?c(q)‖vcb‖‖axbq‖ with a,b in the unit ball of the Schatten class S2q. |
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Keywords: | Operator space Operator Hilbert space Completely p-summing map |
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