Complex Interpolation between Hilbert Banach and Operator Spaces is popular PDF and ePub book, written by Gilles Pisier in 2010-10-07, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Complex Interpolation between Hilbert Banach and Operator Spaces can be Read Online from any device for your convenience.
Complex Interpolation between Hilbert Banach and Operator Spaces Book PDF Summary
Motivated by a question of Vincent Lafforgue, the author studies the Banach spaces $X$ satisfying the following property: there is a function $\varepsilon\to \Delta_X(\varepsilon)$ tending to zero with $\varepsilon>0$ such that every operator $T\colon \ L_2\to L_2$ with $\T\\le \varepsilon$ that is simultaneously contractive (i.e., of norm $\le 1$) on $L_1$ and on $L_\infty$ must be of norm $\le \Delta_X(\varepsilon)$ on $L_2(X)$. The author shows that $\Delta_X(\varepsilon) \in O(\varepsilon^\alpha)$ for some $\alpha>0$ iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of $\theta$-Hilbertian spaces for some $\theta>0$ (see Corollary 6.7), where $\theta$-Hilbertian is meant in a slightly more general sense than in the author's earlier paper (1979).
Detail Book of Complex Interpolation between Hilbert Banach and Operator Spaces PDF
- Author : Gilles Pisier
- Release : 07 October 2010
- Publisher : American Mathematical Soc.
- ISBN : 9780821848425
- Genre : Mathematics
- Total Page : 92 pages
- Language : English
- PDF File Size : 11,9 Mb
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