Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Troitsky, Vladimir G."'
We prove that order convergence on a Boolean algebra turns it into a compact convergence space if and only if this Boolean algebra is complete and atomic. We also show that on an Archimedean vector lattice, order intervals are compact with respect to
Externí odkaz:
http://arxiv.org/abs/2311.15049
It was showed by Donner in 1982 that every order complete vector lattice $X$ may be embedded into a cone $X^s$, called the sup-completion of $X$. We show that if one represents the universal completion of $X$ as $C^\infty(K)$, then $X^s$ is the set o
Externí odkaz:
http://arxiv.org/abs/2306.06248
The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension may be written as an intersection
Externí odkaz:
http://arxiv.org/abs/2210.08805
We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions $C(\Omega)$, $C_b(\Omega)$, $C_0(\Omega)$, and $C^\infty(\Omega)$, extending results of [vdW18]. In particular, it is shown that a sequence uo-c
Externí odkaz:
http://arxiv.org/abs/2110.08709
Autor:
Jardón-Sánchez, Héctor, Laustsen, Niels Jakob, Taylor, Mitchell A., Tradacete, Pedro, Troitsky, Vladimir G.
We prove the existence of free objects in certain subcategories of Banach lattices, including $p$-convex Banach lattices, Banach lattices with upper $p$-estimates, and AM-spaces. From this we immediately deduce that projectively universal objects exi
Externí odkaz:
http://arxiv.org/abs/2101.03510
We characterize the Archimedean vector lattices that admit a positively homogeneous continuous function calculus by showing that the following two conditions are equivalent for each $n$-tuple $\boldsymbol{x} = (x_1,\ldots,x_n)\in X^n$, where $X$ is a
Externí odkaz:
http://arxiv.org/abs/1901.07522
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Akademický článek
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We prove that Krivine's Function Calculus is compatible with integration. Let $(\Omega,\Sigma,\mu)$ be a finite measure space, $X$ a Banach lattice, $x\in X^n$, and $f\colon\mathbb R^n\times\Omega\to\mathbb R$ a function such that $f(\cdot,\omega)$ i
Externí odkaz:
http://arxiv.org/abs/1712.09328
Publikováno v:
In Topology and its Applications 1 March 2022 308
