Introduction to Tensor Products of Banach Spaces

By R. Ryan. 2002

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Some techniques on nonlinear analysis and applications (2010, background): “The same task was brilliantly done, one year later, by J. Lindenstrauss and A. Pe lczyński’s paper [37] which reformulated Grothendieck’s tensorial arguments giving birth to a comprehensible theory with broad applications in Banach Space Theory.”
Unbounded Violation of Tripartite Bell Inequalities (2007, background): “Since then, several important contributions have been made (see [22 ]o r [ 64 ] for a modern reference).”
Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs* (2011, background): “The proof of this theorem can be found in Appendix A of Schwab and Stevenson (2009), or in Hoang and Schwab (2010b).”
The p-approximation property in terms of density of finite rank operators (2009, methodology): “We refer to the Lindenstrauss and Tzafriri and Ryan’s books [13,21] for the classical approximation properties and to Pietsch’s book [16] for operator ideals (see also [6] by Diestel, Jarchow, and Tonge for common operator ideals as Np and Pp , and [15] by Persson and Pietsch for QNp).”
Tests for separability in nonparametric covariance operators of random surfaces (2015, background): “)b(t,t′), that is, (A ⊗eB)u(s,t) = RR [0,1]2 k(s,t,s ′,t′)u(s′,t′)dsdt. E.2 Random Elements in Banach Spaces We understandrandom elements of a separable Banach space (B,k· )in the Bochner sense (e.g. Ryan 2002). A randomelement X ∈ B satisfying EkXk < ∞has a mean EX ∈ B, which satisﬁes S(EX) = E(”
MIONet: Learning multiple-input operators via tensor product (2022, background): “We also refer the reader to [39] for more details.”
Non-Archimedean analytic geometry as relative algebraic geometry (2013, methodology): “In the Archimedean case it is given (see Chapter 2 of [40]) by the completion of the algebraic tensor product V ⊗k W with respect to the norm”
Pentes des fibr\'es vectoriels ad\'eliques sur un corps global (2006, positive): “Cela définit une norme tensorielle d’ordre 2 (voir [29]) et, pour p = 2, la norme g2 est une norme tensorielle hermitienne au sens ci-dessus.”
A characterisation of the Daugavet property in spaces of Lipschitz functions (2017, background): “For a detailed treatment and applications of tensor products, we refer the reader to [27].”