TY - JOUR

T1 - A Maurey type result for operator spaces

AU - Junge, Marius

AU - Lee, Hun Hee

N1 - Funding Information:
✩ Marius Junge is partially supported by the National Science Foundation Foundation DMS 05-56120. Hun Hee Lee is partially supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005-214-C00176). * Corresponding author. E-mail addresses: junge@math.uiuc.edu (M. Junge), lee.hunhee@gmail.com (H.H. Lee).

PY - 2008/3/1

Y1 - 2008/3/1

N2 - The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C (K) and ℓ2 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 v : K → OH is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem: every cb-map v : K → OH is (q, cb)-summing for any q > 2 and hence admits a factorization {norm of matrix} v (x) {norm of matrix} ≤ c (q) {norm of matrix} v {norm of matrix}cb {norm of matrix} a x b {norm of matrix}q with a, b in the unit ball of the Schatten class S2 q.

AB - The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C (K) and ℓ2 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 v : K → OH is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem: every cb-map v : K → OH is (q, cb)-summing for any q > 2 and hence admits a factorization {norm of matrix} v (x) {norm of matrix} ≤ c (q) {norm of matrix} v {norm of matrix}cb {norm of matrix} a x b {norm of matrix}q with a, b in the unit ball of the Schatten class S2 q.

KW - Completely p-summing map

KW - Operator Hilbert space

KW - Operator space

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U2 - 10.1016/j.jfa.2007.11.003

DO - 10.1016/j.jfa.2007.11.003

M3 - Article

AN - SCOPUS:38649134181

SN - 0022-1236

VL - 254

SP - 1373

EP - 1409

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

ER -