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We clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho, and the GFDA spaces introduced in our earlier paper on differentiability of Lipschitz maps into Banach spaces.
If $mu_1,mu_2,dots$ are positive measures on a measurable space $(X,Sigma)$ and $v_1,v_2, dots$ are elements of a Banach space ${mathbb E}$ such that $sum_{n=1}^infty |v_n| mu_n(X) < infty$, then $omega (S)= sum_{n=1}^infty v_n mu_n(S)$ defines a vec
Admissible vectors lead to frames or coherent states under the action of a group by means of square integrable representations. This work shows that admissible vectors can be seen as weights with central support on the (left) group von Neumann algebr
We study the computational content of the Radon-Nokodym theorem from measure theory in the framework of the representation approach to computable analysis. We define computable measurable spaces and canonical representations of the measures and the i
We prove the differentiability of Lipschitz maps X-->V, where X is a complete metric measure space satisfying a doubling condition and a Poincare inequality, and V is a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new ch
We prove that every isometry between the unit spheres of 2-dimensional Banach spaces extends to a linear isometry of the Banach spaces. This resolves the famous Tingleys problem in the class of 2-dimensional Banach spaces.