Spaceability of the sets of surjective and injective operators between sequence spaces
We investigate algebraic structures within sets of surjective and injective linear operators between sequence spaces, completing results of Aron et al.
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arXiv subjects
Vinícius Fávaro
Publications and source records attributed to Vinícius Fávaro.
Lineability and spaceability: a new approach
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings; for instance, Set Theory, Probability Theory, Functional Analysis, Measure Theory, etc. It is a common feeling that positive results on lineability/spaceability are quite natural (i.e., in general \textquotedblleft large\textquotedblright subspaces can be found inside exotic subsets of vector spaces, in quite different settings) and more restrictive approaches have been persecuted. In this paper we introduce and explore a new approach in this direction.
math.FA↗
Maximal spaceability in topological vector spaces
In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context of spaceability and settle some questions on classical sequence spaces that remained open.
math.FA↗