Stable Banach Spaces and Banach Space Structures, I: Fundamentals

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Indiscernible sequences in Banach space geometry

0. Introduction 2 The impact of logic in Banach space theory 2 The case of model theory 2 Model theory for structures of functional analysis 3 Two famous applications 4 A note on the exposition 4 1. Preliminaries: Banach Space Models 5 Banach space structures and Banach space ultrapowers 5 Positive bounded formulas 7 Approximate satisfaction 8 (1 + )-isomorphism and (1 + )-equivalence of struct...

Stable Banach Spaces and Banach Space Structures, Ii: Forking and Compact Topologies

We study model theoretical stability for structures from functional analysis. We prove a functional-analytic version of the Finite Equivalence Relation Theorem. We also the Stability Spectrum Theorem for Banach space structures.

Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

Composition operators between growth spaces‎ ‎on circular and strictly convex domains in complex Banach spaces‎

‎Let $\Omega_X$ be a bounded‎, ‎circular and strictly convex domain in a complex Banach space $X$‎, ‎and $\mathcal{H}(\Omega_X)$ be the space of all holomorphic functions from $\Omega_X$ to $\mathbb{C}$‎. ‎The growth space $\mathcal{A}^\nu(\Omega_X)$ consists of all $f\in\mathcal{H}(\Omega_X)$‎ ‎such that $$|f(x)|\leqslant C \nu(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$‎ ‎for some constant $C>0$‎...