Tagged Questions
0
votes
1answer
29 views
Can a Accumulation Point be an Eigenvalue?
I have a discrete (separable) infinite dimensional Hilbert Space with a compact operator defined on it. So 0 is an accumulation point (some theorem says so). Can 0 also be an eigenvalue? And how would ...
6
votes
1answer
67 views
Tight Probability on Hilbert space
I am considering the following problem. Let $(X_j)$ be i.i.d. $N(0,1)$ random variables and $H$ a Hilbert space with orthonormal basis $(e_j)$. Let $$X:=\sum_j \frac{X_j e_j}{j}$$
And for any ...
5
votes
1answer
125 views
Show $T$ is compact
$H$ and $K$ are Hilbert Spaces, $(u_n)$ and $(v_n)$ are sequences in $H$ and $K$ respectively. $\sum_{n=1}^{n=\infty} \|u_n\|\|v_n\| $ converges.
$T\colon H\rightarrow K$ is defined by ...
4
votes
1answer
83 views
Is it possible to 'approximate' compact, convex sets in $\ell^2$ by the Hilbert cube
Define $H=\{(x_n)_n\in\ell^2:|x_n|\le \frac1n, n\in\mathbf N\}\subset\ell^2$. This set is known as the Hilbert cube and it is well-known that $H$ is compact, convex and non-empty. Let ...
-1
votes
1answer
124 views
Stone-Cech compactification of the separable Hilbert space
Where can I read about the Stone-Cech compactification of the separable Hilbert space?
2
votes
2answers
131 views
I need to show that $K$ is compact and that $co(K)$ is bounded, but not closed.
Let $x_n$ be a sequence in a Hilbert space such that
$\left\Vert x_n \right\Vert=1$ and $ \langle x_n,\ x_m \rangle =0 $, for all $n \neq m$.
Let $ K= \{ x_n/ n : n \in \mathbb{N} \} \cup \{0\} $.
...
