Strong algebrability of sets of sequences and functions
By A. Bartoszewicz, S. Gła̧b. 2012
87 citations recorded by the source corpus.
We introduce a notion of strong algebrability of subsets of linear algebras. Our main results are the following. The set of all sequences from c0 which are not summable with any power is densely strongly c–algebrable. The set of all sequences in l∞ whose sets of limit points are homeomorphic to the Cantor set is comeager and strongly calgebrable. The set of all non-measurable functions from RR is strongly 2–algebrable. These results complete several ones by other authors, within the modern context of lineability.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/85598dde8553976b91dd9f62652c03601da35ce7
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Nonseparable spaceability and strong algebrability of sets of continuous singular functions (2013, background): “, Banach algebras, etc.) with no linear structure given a priori. This research was earlier initiated by Gurariy [13], [14] and then continued by several authors. See for instance [1], [2], [5], [6], [3], [11], [15]. Recall (see [1]) that, for a topological vector space V , its subset A is said to b”
- Linear subsets of nonlinear sets in topological vector spaces (2013, background): “We also say that a subset M of a linear algebra L is strongly κ-algebrable if there exists a κ-generated free algebra A contained in M ∪ {0} (see [39]).”