Oh-type and Oh-cotype of Operator Spaces and Completely Summing Maps
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X iv :m at h/ 05 02 30 2v 1 [ m at h. FA ] 1 5 Fe b 20 05 OH-TYPE AND OH-COTYPE OF OPERATOR SPACES AND COMPLETELY SUMMING MAPS HUN HEE LEE Abstract. The definition and basic properties of OH-type and OH-cotype of operator spaces are given. We prove that every bounded linear map from C(K) into OH-cotype q (2 ≤ q < ∞) space (including most of commutative Lq-spaces) for a compact set K satisfies completely (q, 2)-summing property, a noncommutative analogue of absolutely (q, 2)-summing property. At the end of this paper, we observe that “OH-cotype 2” is equivalent to the previous definition of “OH-cotype 2” of G. Pisier.
منابع مشابه
Oh-type and Oh-cotype of Operator Spaces
The definition and basic properties of OH-type and OH-cotype of operator spaces are given. We present operator space versions of Maurey’s extension theorem and generalized little Grothendieck’s theorem in terms of these new notions. We also observe that “OH-cotype 2” in this paper is equivalent to the previous definition of “OH-cotype 2” of G. Pisier.
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تاریخ انتشار 2005