Results 1 to 10 of about 893,532 (187)
Free Banach lattices under convexity conditions. [PDF]
Rev R Acad Cienc Exactas Fis Nat A Mat, 2022 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.
Jardón-Sánchez H +4 more
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Applications for Unbounded Convergences in Banach Lattices
Fractal and Fractional, 2022 Several recent papers investigated unbounded convergences in Banach lattices. The focus of this paper is to apply the results of unbounded convergence to the classical Banach lattice theory from a new perspective.
Zhangjun Wang, Zili Chen
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Lattice embeddings in free Banach lattices over lattices [PDF]
Mathematical Inequalities & Applications, 2022 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 $i\colon \mathbb{L} \longrightarrow \mathbb{M}$ between two lattices $\mathbb{L} \subseteq \mathbb{M}$ induces a Banach lattice homomorphism $\hat \imath\colon FBL \langle \mathbb{L} \rangle ...
Avilés, Antonio +3 more
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Free complex Banach lattices [PDF]
Journal of Functional Analysis, 2023 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 of $E$ and satisfying the following universal property: for every complex Banach lattice $X_ ...
David de Hevia, Pedro Tradacete
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Geometric Characterization of Injective Banach Lattices
Mathematics, 2021 This is a continuation of the authors’ previous study of the geometric characterizations of the preduals of injective Banach lattices. We seek the properties of the unit ball of a Banach space which make the space isometric or isomorphic to an injective ...
Anatoly Kusraev, Semën Kutateladze
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Valuations on Banach Lattices [PDF]
International Mathematics Research Notices, 2018 Abstract We provide a general framework for the study of valuations on Banach lattices. This complements and expands several recent works about valuations on function spaces, including $L_p(\mu )$, Orlicz spaces, and spaces $C(K)$ of continuous functions on a compact Hausdorff space.
Tradacete, Pedro, Villanueva, Ignacio
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Journal of the European Mathematical SocietyWe investigate the structure of the free p -convex Banach lattice {\mathrm{FBL}}^{(p)}[E] over a Banach space E .
Timur Oikhberg +3 more
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Weak precompactness in Banach lattices [PDF]
Positivity (Dordrecht), 2022 We show that the solid hull of every weakly precompact set of a Banach lattice E is weakly precompact if and only if every order interval in E is weakly precompact, or equivalently, if and only if every disjoint weakly compact set is weakly precompact ...
Bo Xiang, Jinxi Chen, Lei Li
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Grothendieck-type subsets of Banach lattices [PDF]
, 2021 In the setting of Banach lattices the weak (resp. positive) Grothendieck spaces have been defined. We localize such notions by defining new classes of sets that we study and compare with some quite related different classes.
P. Galindo, V. Miranda
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Disjointly non-singular operators on order continuous Banach lattices complement the unbounded norm topology [PDF]
, 2021 In this article we investigate disjointly non-singular (DNS) operators. Following [9] we say that an operator T from a Banach lattice F into a Banach space E is DNS, if no restriction of T to a subspace generated by a disjoint sequence is strictly ...
Eugene Bilokopytov
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