Work

Geometric spaceability in sequence classes and operator ideals

Year: 2026

Type: article

Abstract: This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of Standard Sequence Classes to provide an environment that unifies numerous classical sequence spaces while preserving their fundamental behavior. Utilizing this framework, we prove general $$(\alpha , \mathfrak {c})$$ ( α , c ) -spaceability results for complements of unions of (quasi-)Banach sequence spaces. These results extend the existing literature by addressing the challenging case where $$\alpha > 1$$ α > 1 and by encompassing the non-locally convex (quasi-)Banach setting. Furthermore, we provide criteria for the pointwise $$\mathfrak {c}$$ c -spaceability of differences between general components of operator ideals with values in standard sequence spaces. Our results recover and improve several known findings in the context of vector-valued sequences.

Source: Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas

DOI: 10.1007/s13398-026-01918-1

Authors: Nacib G. Albuquerque, Jamilson R. Campos, Luiz Felipe P. Sousa

Institution: Universidade Federal da Paraíba

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico