Every Separable Banach Space is Isometric to a Space of Continuous Nowhere Differentiable Functions
From MaRDI portal
Publication:4874257
DOI10.2307/2161889zbMath0844.46007OpenAlexW4245513050WikidataQ60356727 ScholiaQ60356727MaRDI QIDQ4874257
Publication date: 12 August 1996
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2161889
every separable Banach space is isometric to a space of continuous nowhere differentiable functionsisometric linear embeddings
Isometric theory of Banach spaces (46B04) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)
Related Items (32)
The topological entropy of Banach spaces ⋮ Stability and robust stabilization of 2-D continuous-discrete systems in Roesser model based on KYP lemma ⋮ Continuous nowhere Hölder functions on ℤ_{𝕡} ⋮ Linear structure of sets of divergent sequences and series ⋮ Lineability and spaceability of sets of functions on $\mathbb {R}$ ⋮ On lineability of sets of continuous functions ⋮ Fixed point properties of \(C^{*}\)-algebras ⋮ Vector spaces of non-measurable functions ⋮ Independent Bernstein sets and algebraic constructions ⋮ Dense-lineability in spaces of continuous functions ⋮ Lineability, spaceability, and additivity cardinals for Darboux-like functions ⋮ Spaceability of the set of continuous injections from \(B_{\ell_p}\) into \(\ell_p\) with nowhere continuous inverses ⋮ Divergence behavior of sequences of linear operators with applications ⋮ Nowhere Hölderian functions and Pringsheim singular functions in the disc algebra ⋮ Lineability, continuity, and antiderivatives in the non-Archimedean setting ⋮ Some results and open questions on spaceability in function spaces ⋮ Lineability of sets of nowhere analytic functions ⋮ On subspaces of \(C[0, 1\) consisting of nonsmooth functions] ⋮ \(c_0\) is isometrically isomorphic to a subspace of Cantor-Lebesgue functions ⋮ Lineability and additivity in \(\mathbb R^{\mathbb R}\) ⋮ Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces ⋮ Algebras in sets of queer functions ⋮ The Besov subspace consisting of most non-smooth functions ⋮ Nonlinear subsets of function spaces and spaceability ⋮ A note on the geometry of certain classes of linear operators ⋮ Banach spaces of fractal functions and trajectories of Brownian motions ⋮ Linearity of sets of strange functions ⋮ Algebrability and nowhere Gevrey differentiability ⋮ The resonance theorem for subspaces ⋮ Linear subsets of nonlinear sets in topological vector spaces ⋮ Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions ⋮ Lineability of non-differentiable Pettis primitives
This page was built for publication: Every Separable Banach Space is Isometric to a Space of Continuous Nowhere Differentiable Functions