Type and cotype of operator spaces
نویسندگان
چکیده
منابع مشابه
Type and Cotype of Operator Spaces
We consider two operator space versions of type and cotype, namely Sp-type, Sq-cotype and type (p, H), cotype (q, H) for a homogeneous Hilbertian operator space H and 1 ≤ p ≤ 2 ≤ q ≤ ∞, generalizing “OH-cotype 2” of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and Lp spaces, and we investigate the relationship between a homogeneous Hilbertian space H and operator spa...
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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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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 c...
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Type and cotype are computed for Banach spaces generated by some positive sublinear operators and Banach function spaces. Applications of the results yield that under certain assumptions Clarkson’s inequalities hold in these spaces.
متن کاملQUOTIENTS OF BANACH SPACES OF COTYPE q
Let Z be a Banach space and let X c Z be a ¿-convex subspace (equivalently, assume that X does not contain /¡"s uniformly). Then every Bernoulli series 2¡?_! e„z„ which converges almost surely in the quotient Z/X can be lifted to a Bernoulli series a.s. convergent in Z. As a corollary, if Z is of cotype q, then Z/X is also of cotype q. This extends a result of [4] concerning the particular case...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2008
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm185-3-2