Work

Copies of $$c_0$$ and $$\ell _\infty $$ in Banach spaces of $$w^*$$-$$w$$-continuous symmetric multilinear maps

Year: 2026

Type: article

Abstract: We study copies of the classical sequence spaces $$c_0$$ and $$\ell _\infty $$ in spaces of $$w^*$$ - $$w$$ continuous symmetric n -linear mappings. More precisely, we consider the Banach space $$\mathcal {L}_{w^*s}(^n X^*, Y)$$ of all $$w^*$$ - $$w$$ continuous symmetric n -linear mappings from $$X^*$$ into Y , together with its closed subspace $$\mathcal {K}_{w^*s}(^nX^*,Y)$$ consisting of compact operators. We prove that $$\ell _\infty $$ embeds in $$\mathcal {K}_{w^*s}(^nX^*,Y)$$ if and only if $$\ell _\infty $$ embeds into either X or Y . As an application of this, we prove that if $$c_{0}$$ embeds in $$K_{w^*s}(^nX^*,Y)$$ , then $$\mathcal {K}_{w^*s}(^nX^*,Y)=\mathcal {L}_{w^*s}(^n X^*, Y)$$ if and only if only one of the following statements is true: $$c_{0}$$ embeds in Y and X has the Schur property, $$c_{0}$$ embeds in X and Y has the Schur property.

Source: Rendiconti del Circolo Matematico di Palermo Series 2

DOI: 10.1007/s12215-026-01397-8

Authors: Michael A. Rincón-Villamizar, Sergio A. Pérez, Diego J. Reyes-Rojas

Institutions: Universidad Industrial de Santander, Universidade de São Paulo

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Universidad Industrial de Santander