Implicit Functions from Topological Vector Spaces to Banach Spaces [PDF]
arXiv, 2003 We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological vector spaces to Banach spaces.
arxiv
Factorization Theorem through a Dunford-Pettis $p$-convergent operator [PDF]
arXiv, 2020 In this article, we introduce the notion of $p$-$(DPL)$ sets.\ Also, a factorization result for differentiable mappings through Dunford-Pettis $p$-convergent operators is investigated.\ Namely, if $ X ,Y $ are real Banach spaces and $U$ is an open convex subset of $X,$ then we obtain that, given a differentiable mapping $f: U\rightarrow Y$ its ...
arxiv
The Frolicher--Kriegl differentiabilities as a particular case of the Bertram--Glockner--Neeb construction [PDF]
arXiv, 2008 We prove that the order $k$ differentiability classes for $k=0,1,...\infty$ in the "arc-generated" interpretation of the Lipschitz theory of differentiation by Frolicher and Kriegl can be obtained as particular cases of the general construction by Bertram, Glockner and Neeb leading to $C^k$ differentiabilities from a given $C^0$ concept.
arxiv
Comparison of some notions of C^k-maps in multi-variable non-archimedian analysis [PDF]
arXiv, 2006 Various definitions of C^k-maps on open subsets of finite-dimensional vector spaces over a complete valued field have been proposed in the literature. We show that the C^k-maps considered by Schikhof and De Smedt coincide with those of Bertram, Glockner and Neeb.
arxiv
Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property [PDF]
arXiv, 2008 We prove the differentiability of Lipschitz maps X-->V, where X is a complete metric measure space satisfying a doubling condition and a Poincar\'e inequality, and V is a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional ...
arxiv
Properties of Hadamard directional derivatives: Denjoy-Young-Saks theorem for functions on Banach spaces [PDF]
arXiv, 2013 The classical Denjoy-Young-Saks theorem on Dini derivatives of arbitrary functions $f: \R \to \R$ was extended by U.S. Haslam-Jones (1932) and A.J. Ward (1935) to arbitrary functions on $\R^2$. This extension gives the strongest relation among upper and lower Hadamard directional derivatives $f^+_H (x,v)$, $f^-_H (x,v)$ ($v \in X$) which holds almost ...
arxiv
Injective Envelopes of Separable C*-algebras [PDF]
arXiv, 2005 Characterisations of those separable C*-algebras that have type I injective envelopes or W*-algebra injective envelopes are presented.
arxiv
An invitation to model theory and C*-algebras [PDF]
arXiv, 2017 We present an introductory survey to first order logic for metric structures and its applications to C*-algebras.
arxiv
Orthogonality: An antidote to Kadison's anti-lattice theorem [PDF]
arXiv, 2019 In this paper, we propose non-commutative analogues of infimum and supremum with the help of algebraic orthogonality.
arxiv
Boundary Representations for Operator Algebras [PDF]
arXiv, 2001 All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C*-envelope.
arxiv