Related papers: A note on nonseparable Lipschitz-free spaces

A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…

In this paper we study the properties of P-generated spaces (by analogy with compactly generated). We prove that a regular Lindel\"of generated space with uncountable dispersion character is resolvable. It is proved that Hausdorff…

We extend the well-known criterion of Lotz for the dual Radon-Nikodym property (RNP) of Banach lattices to finitely generated Banach $C(K)$-modules and Banach $C(K)$-modules of finite multiplicity. Namely, we prove that if $X$ is a Banach…

We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then…

We show that for every complete metric space $M$ there exists another complete metric space $N$ of the same density character such that the curve-flat quotient of $N$ is isometric to $M$. Moreover, we show that if $M$ is compact and…

We prove that every separable Banach space has a barrelled subspace with algebraic dimension $\mathrm{non}(\mathcal M)$, which denotes the smallest cardinality of a non-meager subset of $\mathbb R$. This strengthens a theorem of Sobota.…

It is shown that any Banach space X of sufficiently large density contains an (infinite) unconditional sequence and a separable quotient. If a density of X is a weakly compact cardinal, then X contains an unconditional sequence of…

In the main result of the paper we extend Rosenthal's characterization of Banach spaces with the Schur property by showing that for a quasi-complete locally convex space $E$ whose separable bounded sets are metrizable the following…

The Grothendieck property has become important in research on the definability of pathological Banach spaces [CI], [HT], and especially [HT20]. We here answer a question of Arhangel'ski\u{\i} by proving it undecidable whether countably…

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is…

We consider several quantities related to weak sequential completeness of a Banach space and prove some of their properties in general and in $L$-embedded Banach spaces, improving in particular an inequality of G. Godefroy, N. Kalton and D.…

We show that for a $\sigma $-ideal $\ci$ with a Steinhaus property defined on Banach space, if two non-homeomorphic Banach with the same cardinality of the Hamel basis then there is a $\ci$ nonmeasurable subset as image by any isomorphism…

In this paper, we first introduce $\mathbb{L}$-$\mu$-measurable functions and $\mathbb{L}$-Bochner integrable functions on a finite measure space $(S,\mathcal{F},\mu),$ and give an $\mathbb{L}$-valued analogue of the canonical…

We give a construction under $CH$ of a non-metrizable compact Hausdorff space $K$ such that any uncountable semi-biorthogonal sequence in $C(K)$ must be of a very specific kind. The space $K$ has many nice properties, such as being…

We prove the equivalence of two seemingly very different ways of generalising Rademacher's theorem to metric measure spaces. One such generalisation is based upon the notion of forming partial derivatives along a very rich structure of…

In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the…

We prove that the following three properties for a Banach space are all different from each other: every finite convex combination of slices of the unit ball is (1) relatively weakly open, (2) has nonempty interior in relative weak topology…

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions,…

We give a sharp condition on the lower local Lipschitz constant of a mapping from a metric space supporting a Poincar\'e inequality to a Banach space with the Radon-Nikodym property that guarantees differentiability at almost every point.…

We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with…