On the category of quotient Banach spaces after Wegner
We study Waelbroeck's category of Banach quotients after Wegner, focusing on its basic homological and functional analytic properties.
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arXiv subjects
José Navarro Garmendia
Publications and source records attributed to José Navarro Garmendia.
Isometries of ultrametric normed spaces
We show that the group of isometries of an ultrametric normed space can be seen as a kind of a fractal. Then, we apply this description to study ultrametric counterparts of some classical problems in Archimedean analysis, such as the so called Problème des rotations de Mazur or Tingley's problem. In particular, it turns out that, in contrast with the case of real normed spaces, isometries between ultrametric normed spaces can be very far from being linear.
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Corrigendum to "On the Mazur-Ulam theorem in non-Archimedean fuzzy anti-2-normed spaces"
In this note we correct a paper by D. Kang ("On the Mazur-Ulam theorem in non-Archimedean fuzzy anti-2-normed spaces", Filomat, 2017). The research in that paper applies to what the author calls strictly convex spaces. Nevertheless, we prove that this notion is void: there is no single space that satisfies the definition.
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A precision on the concept of strict convexity in non-Archimedean analysis
We prove that the only non-Archimedean strictly convex spaces are the zero space and the one-dimensional linear space over $\, \mathbb{Z}/3\mathbb{Z}$, with any of its trivial norms.
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Voidness of strict convexity in non-Archimedean fuzzy normed spaces
In this short note, we show by elementary computations that the notion of non-Archimedean fuzzy normed (and 2-normed) spaces is void. Namely, there are no strictly convex spaces at all --not even the zero-dimensional linear space. Before this, we also study the case of strictly convex non-Archimedean normed spaces; in this setting we see that the only nonzero linear space (defined over an arbitrary non-Archimedean field) that satisfies this property is the one-dimensional linear space over $\mathbb{Z}/3\mathbb{Z}$. Consequently, the results that have been proven for this class of spaces, like the Mazur-Ulam Theorem, are either trivial or empty statements.
math.FA↗