论文标题
Banach Halos和短异构体
Banach halos and short isometries
论文作者
论文摘要
本文的目的是双重的。首先，我们制定了Banach Halo的概念，类似于Banach环的概念，但通常的三角形不平等被不平等$ | a + b |取代。 \ leq（| a |，| b |）_p $涉及一些$ p \ in] 0， +\ infty] $的p-norm，或不等式$ | a +b | \ leq c \ max c \ max（| a |，| b |）$。这使我们能够在Banach Halos上具有一定的力量，例如，在$ \ Mathbb {Z} $上使用通常的绝对值的正方形。然后，我们定义并研究了基础交换性Banach Halo的规范参与膜的短异构体。该理论的目的是定义一个可代表的组$ k_n \ subset {\ rm gl} _n $，其点的点为$ \ mathbb {r} $ give $ o_n（\ mathbb {r}）$，其点的点为$ \ nathbb {q} _p $ _p $ _ b $ _n（qud）在这两组之间一种几何解释。
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 $|a+b|\leq C\max(|a|,|b|)$. 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 $K_n\subset {\rm GL}_n$ 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.
