Weak type $(2,H)$ and weak cotype $(2,H)$ of operator spaces

Details Weak type $(2,H)$ and weak cotype $(2,H)$ of operator spaces Weak type $(2,H)$ and weak cotype $(2,H)$ of operator spaces

2005-02-16

arxiv.org/abs/math/0502337v3

Mathematics

Functional Analysis

22 pages, Definition is broadened, and eigen value estimation for weak $H$-space has been added. Tsirelson type construction i

Scientific paper

Recently an operator space version of type and cotype, namely type $(p,H)$ and cotype $(q,H)$ of operator spaces for $1\leq p \leq 2\leq q \leq \infty$ and a subquadratic and homogeneous Hilbetian operator space $H$ were introduced and investigated by the author. In this paper we define weak type $(2,H)$ (resp. weak cotype $(2,H)$) of operator spaces, which lies strictly between type $(2,H)$ (resp. cotype $(2,H)$) and type $(p,H)$ for all $1\leq p <2$ (resp. cotype $(q,H)$ for all $2

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