On Disjointly Singular Centralizers

Author(s)

Castillo, Jesus M. F. ; Cuellar, Wilson ; Ferenczi, Valentin ; Moreno, Yolanda

• Document type: Journal article
• Source: Israel Journal of Mathematics; v. 252, n. 1, p. 27-pg., 2022-09-09.

Abstract

We study "disjoint" versions of the notions of trivial, locally trivial, strictly singular and super-strictly singular quasi-linear maps in the context of Kothe function spaces. Among other results, we show: (i) (locally) trivial and (locally) disjointly trivial notions coincide on reflexive spaces; (ii) on non-atomic superreflexive Kothe spaces, no centralizer is singular, although most are disjointly singular. (iii) no supersingular quasi-linear maps exist between superreflexive spaces although Kalton-Peck centralizers are super-disjointly singular; (iv) disjoint singularity does not imply super-disjoint singularity. (AU)

• FAPESP's process: 16/25574-8 - Geometry of Banach Spaces
• Grantee: Valentin Raphael Henri Ferenczi
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/17216-1 - Twisted sums and group representations in Banach spaces
• Grantee: Valentin Raphael Henri Ferenczi
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 18/18593-1 - Homological and descriptive set theory methods in Banach spaces
• Grantee: Wilson Albeiro Cuellar Carrera
• Support Opportunities: Regular Research Grants