C*-Algebras and Factorization Through Diagonal Operators
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AbstractLet A be a C*-algebra and E be a Banach space with the Radon-Nikodym property. We prove that if j is an embedding of E into an injective Banach space then for every absolutely summing operator T : A → E, the composition j ○ T factors through a diagonal operator from l2 into l1. In particular, T factors through a Banach space with the Schur property. Similarly, we prove that for 2 < p < ∞, any absolutely summing operator from A into E factors through a diagonal operator from lp into l2.
1993 ◽
Vol 54
(2)
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pp. 213-220
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1981 ◽
Vol 90
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pp. 63-70
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2001 ◽
Vol 6
(5)
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pp. 309-315
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2011 ◽
Vol 54
(2)
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pp. 515-529
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2004 ◽
Vol 76
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pp. 269-280
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1991 ◽
Vol 33
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pp. 223-230
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