All Questions

It is easy to see that for any $x$ and $y$ on the unit sphere of a Hilbert space $H$ there exists a surjective isometry $U$ such that $Ux=y$. Does something more general also hold? That is, given two ...

There are plenty of isometric embeddings of metric spaces in Banach spaces. Nevertheless, I have been unable to find any significant result on isometric embeddings into Hilbert spaces. My question is: ...

Let $S$ be a (unit) sphere in a Hilbert Space $H$ with $\dim H \ge 3$. Let $A \subset S$ have the following properties: $A$ is connected; The affine hull of $A$ is the whole space; For every $x,y\in ...

Suppose I have a family of $n$ linearly-independent elements $v_i$ of the Hilbert space $\mathbb{C}^m$, which are not necessarily orthogonal. Can I always find a partial isometry $f: \mathbb{C} ^m \to ...