Related papers: Pointwise Lineability in Sequence Spaces
It is proved the existence of large algebraic structures \break --including large vector subspaces or infinitely generated free algebras-- inside, among others, the family of Lebesgue measurable functions that are surjective in a strong…
We investigate dense lineability and spaceability of subsets of $\ell_\infty$ with a prescribed number of accumulation points. We prove that the set of all bounded sequences with exactly countably many accumulation points is densely…
The essence of the notion of lineability and spaceability is to find linear structures in somewhat chaotic environments. The existing methods, in general, use \textit{ad hoc} arguments and few general techniques are known. Motivated by the…
This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of \emph{Standard Sequence Classes} to provide an environment that unifies numerous…
In this paper, we introduce cone normed linear space, study the cone convergence with respect to cone norm. Finally, we prove the completeness of a finite dimensional cone normed linear space.
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…
In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set…
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…
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;…
Some new bounds for Cebysev functional for sequences of vectors in normed linear spaces are pointed out.
This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…
We investigate lineability/spaceability problems within the setting of multilinear summing operators on quasi-Banach sequence spaces. Furthermore, we deal with the contemporary geometric notions of pointwise-lineability and…
In this note we generalize a criterion within the concept of infinite dense lineability due to Calder\'on-Moreno, Gerlach-Mena and Prado-Bassas. We also introduce and explore some local notions of lineability.
In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.
We develop an analog to the ends of a metric space for the category of coarse metric spaces and show that it is equivalent to a previously defined coarse invariant.
This note presents an extension of a result within the concept of [S]-lineability, originally developed in 2019 by L. Bernal-Gonz\'alez, J.A. Conejero, M. Murillo-Arcila, and J.B. Seoane-Sep\'ulveda . Additionally, we provide a…
We investigate algebraic structures within sets of surjective and injective linear operators between sequence spaces, completing results of Aron et al.
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in…
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.