Remarks on non linear type and Pisier's inequality

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Bridgeland-stable moduli spaces for $K$-trivial surfaces (2007, unknown): “3 have been obtained for the notions of type and cotype of Banach spaces (see [6, 30, 1, 25, 24, 22]), and have been used to transfer some of the linear theory to the setting of general metric spaces.”
Embeddings of Discrete Groups and the Speed of Random Walks (2007, background): “We refer to [15, 10, 7, 28, 26, 27] and the references therein for background on this topic and many applications.”
Analysis in Banach Spaces (2023, result): “Earlier R-boundedness results for the range of a bounded representation π : C(K)→ L (X) appeared in De Pagter and Ricker [2007]. Related results can be found in Kriegler and Le Merdy [2010].”
Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces (2004, methodology): “In [56] it is shown that if X is a UMD Banach space (see [10] for details on UMD spaces) of Rademacher type p, then X also has Enflo type p.”
Euclidean quotients of finite metric spaces (2004, background): “By the results of [16] and [22], it follows that cp(U) ≥ cp(C) ≥ a(p)kmin{1−1/p,1/2}, for some constant a(p) depending only on p.”
Comparison of Metric Spectral Gaps (2013, background): “The link between these notions and Ball’s notion of Markov type is that Markov type p implies En o type p (see [82]).”