Free Banach lattices under convexity conditions
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. Math. 2019). In the p-convex and AM-space cases, we are able to explicitly identify the norms of the free Banach lattices, and we conclude by investigating the structure of these norms in connection with nonlinear p-summing maps.
1979 ◽
Vol 35
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pp. 264-281
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2008 ◽
Vol 344
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pp. 851-856
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1993 ◽
Vol 35
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pp. 207-217
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2016 ◽
Vol 290
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pp. 1544-1552
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