All Questions

I am interested in generalisations to Banach spaces of the following construction, which relates to the singular value decomposition of a finite-dimensional linear map. If $V$, $W$ are finite-...

Let $E$ be a real normed space, and let $v_1,...,v_n\in E$ be linearly independent. The parallelepiped defined by these vectors is $P=\{\sum_{i=1}^{n}\alpha_i v_i|~0\le\alpha_i\le 1\}$. Since $E$ is a ...

Let $(X,\|\cdot\|)$ be a real normed space. For any points $A$ and $B$ in $X$, let $AB:=\|A-B\|$. Suppose that for any points $A$ and $B$ in $X$ and any straight line $\ell\subseteq X$ such that $B\...

This concrete geometric question has arisen out of the problem of counting arithmetic functions with a particular property. The details of the relationship between the counting procedure and this ...