论文标题
准菌群在有限维空间上的Banach空间
The Banach space of quasinorms on a finite-dimensional space
论文作者
论文摘要
我们的主要结果指出，在有限维矢量空间$ e $的情况下，在连续式准词集中定义的伪测量值$ \ MATHCAL {q} _0 = \ {\ | \ | \ cdot \ |： $ d（\ | \ cdot \ | _x，\ | \ cdot \ | _y）= \ min \ {μ：\ | \ cdot \ cdot \ | | _x \ | \leqλ\ | \ | \ cdot \ cdot \ cdot \ | __y \ | _y \ leq \ leq leq \ cdot \ | \ cdot \ | \ cdot \ cdot \ | _ coft oftere当我们采用明显的商$ \ mathcal {q} = \ mathcal {q} _0/\！\ sim $时，规范并在$ \ Mathcal {q} $上定义了适当的操作。 我们用一些解释了该空间和Banach-Mazur契约的相关性，并进行了一些解释。
Our main result states that, given a finite-dimensional vector space $E$, the pseudometric defined in the set of continuous quasinorms $\mathcal{Q}_0=\{\|\cdot\|:E\to\mathbb{R}\}$ as $$d(\|\cdot\|_X,\|\cdot\|_Y)=\min\{μ:\|\cdot\|_X \leqλ\|\cdot\|_Y\leqμ\|\cdot\|_X\text{ for some }λ\}$$ induces, in fact, a complete norm when we take the obvious quotient $\mathcal{Q}=\mathcal{Q}_0/\!\sim$ and define the appropriate operations on $\mathcal{Q}$. We finish the paper with a little explanation of how this space and the Banach-Mazur compactum are related.
