Most books about topological vector spaces talk only about those that are over $\mathbb{R}$ or $\mathbb{C}$ with their usual topologies. I'm curious about the theory of such spaces in more general over other topological fields (ie over $\mathbb{R}$ or $\mathbb{C}$ with non-euclidean topologies or over other fields altogether). What are some references on this topic?
$\begingroup$
$\endgroup$
2
asked Jan 30, 2022 at 22:55
-
$\begingroup$ Maybe it is a situation like the inner product space $\endgroup$– Reine AbstraktionSep 30, 2022 at 16:24
-
$\begingroup$ $p$-adic numbers would be an interesting example. $\endgroup$– Thomas AndrewsSep 30, 2022 at 21:02
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Some classic texts ...
Narici, Lawrence; Beckenstein, Edward, Banach algebras over valued fields, Approximation theory and functional analysis, Proc. int. Symp., Campinas 1977, Math. Stud., North-Holland 35, 333-342 (1979). ZBL0397.46071.
Narici, L.; Beckenstein, E.; Bachman, G., Functional analysis and valuation theory, Pure and Applied Mathematics 5. New York: Marcel Dekker VI, 192 p. (1971). ZBL0218.46004.
Alling, Norman L., Fundamentals of analysis over surreal numbers fields, Rocky Mt. J. Math. 19, No. 3, 565-573 (1989). ZBL0709.12001.
