Lineability and algebrability of pathological phenomena in analysis

By F. J. García-Pacheco, N. Palmberg, J. B. Seoane-Sep'ulveda. 2007

52 citations recorded by the source corpus.

We show that, in analysis, many pathological phenomena occur more often than one could expect, that is, in a linear or algebraic way. We show this by means of the construction of large algebraic structures (infinite dimensional vector spaces or infinitely generated algebras) enjoying some special or pathological properties.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e715acafec31b8ab27814aa25bc6bbbebcc8042b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Daniel Pellegrino
2. L. González
3. J. Sepúlveda
4. S. Gła̧b
5. A. Bartoszewicz

In Applied Mathematics

1. Daniel Pellegrino
2. L. González
3. J. Sepúlveda
4. S. Gła̧b
5. A. Bartoszewicz

In Mathematical Physics

1. Daniel Pellegrino
2. L. González
3. J. Sepúlveda
4. S. Gła̧b
5. A. Bartoszewicz

Citations in the corpus

• Strong algebrability of sets of sequences and functions (2012, background): “Other algebrability results can be found in [11] and [12].”
• Linear subsets of nonlinear sets in topological vector spaces (2013, background): “More precisely, in [84] Bernal-González and Ordóñez-Cabrera provided a series of conditions on a measure space (Ω,Σ, μ) to ensure the spaceability of the sets Lp(Ω)\ ⋃ q∈[1,p) Lq(Ω), Lp(Ω)\ ⋃ q∈[p,∞) Lq(Ω), and Lp(Ω) \ ⋃ q∈[1,∞)\{p} Lq(μ,X) (for p ≥ 1); whereas in [111] Botelho, Fávaro, Pellegri”