تقرير
L-functional analysis
| العنوان: | L-functional analysis |
|---|---|
| المؤلفون: | Kikianty, Eder, Messerschmidt, Miek, Naude, Luan, Roelands, Mark, Schwanke, Christopher, van Amstel, Walt, van der Walt, Jan Harm, Wortel, Marten |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, 46B99 (Primary), 06F25 (Secondary) |
| الوصف: | Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital $f$-algebra $\mathbb{L}$; such an algebra can be represented as a suitable space of continuous functions. We set up the basic theory of $\mathbb{L}$-normed and $\mathbb{L}$-Banach spaces and bounded operators between them, we discuss the $\mathbb{L}$-valued analogues of the classical $\ell^p$-spaces, and we prove the analogue of the Hahn-Banach theorem. We also discuss the basics of the theory of $\mathbb{L}$-Hilbert spaces, including projections onto convex subsets and the Riesz Representation theorem. Comment: 50 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.10222 |
| رقم الأكسشن: | edsarx.2403.10222 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |