Results 11 to 20 of about 10,159 (123)
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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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. Namely, a Banach lattice $X$ satisfies the lattice-lifting property if every lattice homomorphism to $X$ having a bounded
Avilés, Antonio +3 more
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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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The free Banach lattice generated by a lattice [PDF]
Positivity, 2018 This last version differs from the published version in that it contains a new proof of Lemma 5.3. The previous proof worked for the particular case in which the lemma was applied, but it was wrong for the lemma as stated in ...
Avilés, Antonio +1 more
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The free Banach lattice generated by a Banach space [PDF]
Journal of Functional Analysis, 2018 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 these spaces, answering some recent questions of B. de Pagter and A.W. Wickstead.
Avilés, Antonio +2 more
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Octahedral norms in free Banach lattices [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020 In this paper, we study octahedral norms in free Banach lattices $FBL[E]$ generated by a Banach space $E$. We prove that if $E$ is an $L_1( )$-space, a predual of von Neumann algebra, a predual of a JBW$^*$-triple, the dual of an $M$-embedded Banach space, the disc algebra or the projective tensor product under some hypothesis, then the norm of $FBL[E]
Sheldon Dantas +3 more
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Chain conditions in free Banach lattices [PDF]
Journal of Mathematical Analysis and Applications, 2018 We show that for an arbitrary Banach space $E$, the free Banach lattice $FBL[E]$ generated by $E$ satisfies the $ $-bounded chain condition.
Avilés, Antonio +2 more
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Free dual spaces and free Banach lattices
Journal of Mathematical Analysis and Applications30 pages; includes new result on lattice finite representability of $FBL^p[E^{**}]$ in $FBL^p[E]$
E. García-Sánchez, P. Tradacete
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Free Banach lattices generated by a lattice and projectivity [PDF]
Proceedings of the American Mathematical Society, 2022 In this article we deal with the free Banach lattice F B L ⟨ L ⟩ FBL\langle \mathbb {L} \rangle generated by a lattice L \mathbb {L} . We prove that if F B L ⟨ L ⟩ FBL\langle ...
Avilés, Antonio +3 more
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Lattice embeddings in free Banach lattices over lattices
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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