Results 1 to 10 of about 54,364 (89)
Lattice embeddings in free Banach lattices over lattices [PDF]
Mathematical Inequalities & Applications, 2021 In this article we deal with the free Banach lattice generated by a lattice and its behavior with respect to subspaces. In general, any lattice embedding i : L −→ M between two lattices L ⊆ M induces a Banach lattice homomorphism ı̂ : FBL〈L〉 −→ FBL〈M ...
A. Avil'es +3 more
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A Godefroy—Kalton principle for free Banach lattices [PDF]
Israel Journal of Mathematics, 2021 Motivated by the Lipschitz-lifting property of Banach spaces introduced by Godefroy and Kalton, we consider the lattice-lifting property, which is an analogous notion within the category of Banach lattices and lattice homomorphisms.
A. Avilés +3 more
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Free Banach lattices under convexity conditions. [PDF]
Rev R Acad Cienc Exactas Fis Nat A Mat, 2022 AbstractWe 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 exist in each of these subcategories, extending results of Leung, Li, Oikhberg and Tursi (Israel J ...
Jardón-Sánchez H +4 more
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Free dual spaces and free Banach lattices [PDF]
Journal of Mathematical Analysis and Applications, 2022 The relation between the free Banach lattice generated by a Banach space and free dual spaces is clarified. In particular, it is shown that for every Banach space $E$ the free $p$-convex Banach lattice generated by $E^{**}$, denoted $FBL^p[E ...
Enrique Garc'ia-S'anchez, P. Tradacete
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The free Banach lattice generated by a lattice [PDF]
Positivity, 2018 We introduce the free Banach lattice generated by a lattice $$\mathbb {L}$$L. We give an explicit description of it and we study some of its properties for the case when $$\mathbb {L}$$L is a linear order, like the countable chain condition.
A. Avil'es, J. R. Rodríguez Abellán
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Free complex Banach lattices [PDF]
Journal of Functional Analysis, 2022 The construction of the free Banach lattice generated by a real Banach space is extended to the complex setting. It is shown that for every complex Banach space $E$ there is a complex Banach lattice $FBL_{\mathbb C}[E]$ containing a linear isometric copy
David de Hevia, P. Tradacete
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Free Banach lattices generated by a lattice and projectivity [PDF]
Proceedings of the American Mathematical Society, 2021 In this article we deal with the free Banach lattice FBL〈L〉 generated by a lattice L. We prove that if FBL〈L〉 is projective then L has a maximum and a minimum.
A. Avil'es +3 more
semanticscholar +4 more sources
The free Banach lattice generated by a Banach space [PDF]
Journal of Functional Analysis, 2017 The free Banach lattice over a Banach space is introduced and analyzed. This generalizes the concept of free Banach lattice over a set of generators, and allows us to study the Nakano property and the density character of non-degenerate intervals on ...
A. Avil'es +2 more
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Projectivity of the free Banach lattice generated by a lattice [PDF]
Archiv der Mathematik, 2019 We study the projectivity of the free Banach lattice generated by a lattice $\mathbb{L}$ in two cases: when the lattice is finite, and when the lattice is an infinite linearly ordered set. We prove that in the first case it is projective while in the second case, if the linear order contains either an increasing sequence without upper bounds or a ...
A. Avilés, J. R. Rodríguez Abellán
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Free and projective Banach lattices [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2012 We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms, and establish some of their fundamental properties.
B. de Pagter, A. Wickstead
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