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.