Non-Archimedean John, Non-Archimedean Dvoretzky-Milman, Non-Archimedean Type-Cotype and Non-Archimedean Kwapien Problems
Key Points
This paper examines the possibility of non-Archimedean adaptations of four significant theorems and concepts in functional analysis.
Identification of non-Archimedean adaptations for each theorem.
Comparative analysis with existing Archimedean frameworks.
Theoretical exploration of implications for Banach space properties.
Non-Archimedean counterparts for the John Theorem and Dvoretzky-Milman Theorem are proposed.
Type-Cotype concepts are redefined in the non-Archimedean context.
Potential extensions of the Kwapien Theorem are suggested.
Abstract
We ask for non-Archimedean version of following four: (1) John Theorem, (2) Dvoretzky-Milman Theorem, (3) Type-Cotype of Banach space, (4) Kwapien Theorem.