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- W4308758533 abstract "The aim of this article is twofold. First, we develop the notion of a Banach halo, similar to that of a Banach ring, except that the usual triangular inequality is replaced by the inequality $|a + b| leq (|a| , |b|)_p$ involving the p-norm for some $p in]0, +infty]$, or by the inequality $|a+b|leq Cmax(|a|,|b|)$. This allows us to have a flow of powers on Banach halos and to work, e.g., with the square of the usual absolute value on $mathbb{Z}$. Then we define and study the group of short isometries of normed involutive coalgebras over a base commutative Banach halo. An aim of this theory is to define a representable group $K_nsubset {rm GL}_n$ whose points with values in $mathbb{R}$ give $O_n(mathbb{R})$ and whose points with values in $mathbb{Q}_p$ give GL$_n(mathbb{Z}_p)$, giving to the analogy between these two groups a kind of geometric explanation." @default.
- W4308758533 created "2022-11-15" @default.
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- W4308758533 date "2022-11-09" @default.
- W4308758533 modified "2023-09-30" @default.
- W4308758533 title "Banach halos and short isometries" @default.
- W4308758533 hasPublicationYear "2022" @default.
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