Dense lineability and algebrability of ℓ^{∞}∖𝑐₀

Papathanasiou, Dimitris

doi:10.1090/proc/15758

Dense lineability and algebrability of $\ell ^{\infty }\setminus c_0$
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Proc. Amer. Math. Soc. 150 (2022), 991-996 Request permission

Abstract:

We show that the set $\ell ^{\infty }\setminus c_0$ is maximal dense-lineable and densely strongly $\mathfrak {c}$-algebrable answering a question posed by Nestoridis and complementing a result by García-Pacheco, Martín and Seoane-Sepúlveda.

References

Richard M. Aron, Luis Bernal González, Daniel M. Pellegrino, and Juan B. Seoane Sepúlveda, Lineability: the search for linearity in mathematics, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2016. MR 3445906
Artur Bartoszewicz and Szymon Gła̧b, Strong algebrability of sets of sequences and functions, Proc. Amer. Math. Soc. 141 (2013), no. 3, 827–835. MR 3003676, DOI 10.1090/S0002-9939-2012-11377-2
F. J. García-Pacheco, M. Martín, and J. B. Seoane-Sepúlveda, Lineability, spaceability, and algebrability of certain subsets of function spaces, Taiwanese J. Math. 13 (2009), no. 4, 1257–1269. MR 2543741, DOI 10.11650/twjm/1500405506
V. Nestoridis, A project about chains of spaces, regarding topological and algebraic genericity and spaceability, arXiv:2005.01023, 2020.
Haskell P. Rosenthal, On quasi-complemented subspaces of Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 361–364. MR 227739, DOI 10.1073/pnas.59.2.361
Stephen Willard, General topology, Dover Publications, Inc., Mineola, NY, 2004. Reprint of the 1970 original [Addison-Wesley, Reading, MA; MR0264581]. MR 2048350