Banach Space Theory: The Basis for Linear and Nonlinear Analysis

By Marian J. Fabian, Petr Habala, P. Hájek, V. Montesinos, V. Zizler. 2010

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The algebra of conditional sets and the concepts of conditional topology and compactness (2013, background): “pace if X is conditionally complete for the conditional metric d(x,y) := kx−yk. We will close this paper by showing the conditional version of the Krein-Šmulian Theorem, adapting the argumentation in [11]. A proof of this theorem for L∞-modules can be found in Eisele and Sonia [10]. Since X and its ”
Approximation properties and Schauder decompositions in Lipschitz-free spaces (2012, background): “It follows from the compactness of the unit ball of Lip0(M) with respect to the topology of pointwise convergence, that F(M) can be seen as the canonical predual of Lip0(M).”
MIONet: Learning multiple-input operators via tensor product (2022, background): “We refer the reader to [8] for more details.”
The non-linear geometry of Banach spaces after Nigel Kalton (2012, unknown): “From the recent textbooks that may be used in the area we mention [4] and [29].”