We show that there exist uncountably many (tall and nontall) pairwise nonisomorphic density-like ideals on which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80 (2015), pp. 1268-1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal.
Density-like and Generalized Density Ideals
Leonetti P
;
2022-01-01
Abstract
We show that there exist uncountably many (tall and nontall) pairwise nonisomorphic density-like ideals on which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80 (2015), pp. 1268-1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal.
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