Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions

DOI10.1090/S0002-9939-00-05595-7zbMath0956.26008MaRDI QIDQ4508155

Stanislav Hencl

Publication date: 3 October 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

isometryCantor setBanach spaceHölder functionapproximately differentiable function

Mathematics Subject Classification ID

Isometric theory of Banach spaces (46B04) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items

The topological entropy of Banach spaces ⋮ Continuous nowhere Hölder functions on ℤ_{𝕡} ⋮ Lineability and spaceability of sets of functions on $\mathbb {R}$ ⋮ On lineability of sets of continuous functions ⋮ Vector spaces of non-measurable functions ⋮ On the existing set of the oscillating spectrum ⋮ Dense-lineability in spaces of continuous functions ⋮ Lineability in subsets of measure and function spaces ⋮ Spaceability of the set of continuous injections from \(B_{\ell_p}\) into \(\ell_p\) with nowhere continuous inverses ⋮ 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 ⋮ Algebraic genericity within the class of sup-measurable functions ⋮ Strong \(\mathfrak c\)-algebrability of strong Sierpiński-Zygmund, smooth nowhere analytic and other sets of 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 ⋮ Nonlinear subsets of function spaces and spaceability ⋮ Riemann integrability and Lebesgue measurability of the composite function ⋮ Algebrability, non-linear properties, and special functions ⋮ Banach spaces of fractal functions and trajectories of Brownian motions ⋮ Algebrability and nowhere Gevrey differentiability ⋮ Linear subsets of nonlinear sets in topological vector spaces ⋮ Lineability of non-differentiable Pettis primitives

Cites Work

• Differentiation of Real Functions
• Every Separable Banach Space is Isometric to a Space of Continuous Nowhere Differentiable Functions
• Unnamed Item