Type and cotype of operator spaces

Volume 185 / 2008

Hun Hee Lee Studia Mathematica 185 (2008), 219-247 MSC: Primary 47L25; Secondary 46B07. DOI: 10.4064/sm185-3-2


We consider two operator space versions of type and cotype, namely $S_p$-type, $S_q$-cotype and type $(p,H)$, cotype $(q,H)$ for a homogeneous Hilbertian operator space $H$ and $1\leq p \leq 2 \leq q\leq \infty $, generalizing “$OH$-cotype 2” of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and $L_p$ spaces, and we investigate the relationship between a homogeneous Hilbertian space $H$ and operator spaces with cotype $(2,H)$. As applications we consider operator space versions of generalized little Grothendieck's theorem and Maurey's extension theorem in terms of these new notions.


  • Hun Hee LeeDepartment of Pure Mathematics
    Faculty of Mathematics
    University of Waterloo
    200 University Avenue West
    Waterloo, Ontario, Canada N2L 3G1

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