Maximal Spaceability of the set of non-absolutely summing operators in quasi-Banach spaces

Araujo, Daniel

doi:10.30504/jims.2026.596014.1347

Maximal Spaceability of the set of non-absolutely summing operators in quasi-Banach spaces

Articles in Press

Document Type : Research Article

Author

Daniel Araujo

Department of Mathematics- UFRPE

10.30504/jims.2026.596014.1347

Abstract

For every 0 < p < 1, we establish maximal spaceability of the bounded operators on ‘p

which fail to be (r; s)-absolutely summing for all 1 ≤ s ≤ r < 1, using the coordinate-disjointization

construction and Maddox’s theorem. We give detailed isometric estimates and prove a corresponding

maximal spaceability theorem inside the compact operators. The compact result is based on an explicit

diagonal multiplier and a single weakly 1-summable sequence witnessing the simultaneous failure of

all admissible absolute summability conditions. A diagonal characterization, a logarithmic compact

example, and extensions to operators with values in quasi-Banach spaces containing a copy of ‘p are

also obtained. The constructed subspaces are isomorphic to ‘p and have maximal algebraic dimension

whenever the ambient operator spaces have dimension c.

Keywords

Lineability

Spaceability

Non-absolutely summing operators

quasi-Banach spaces

Compact operators

Subjects