Tagged Questions

Norm is a function on a vector space $X$ which generalizes notion of length of vector in general vector spaces.

283 views

34 views

Equivalences for a Banach lattice

I'm trying to prove the following equivalences for a Banach lattice $E$: $E$ has an order continuous norm Every monotone order bounded sequence in $E$ is convergent E is an ideal in $E^{**}$...
41 views

20 views

21 views

Norm of infinite dimensional Hilbert space to calculate difference between string lengths

I am trying to wrap my head around Proposition 13, last para, page 1049 in this paper. The authors are trying to prove certain properties of string edit distance (defined at the start of Section of 6....
22 views

Find value of $p$ such that $\sum |b_n|^p$ converges

Let $(X , \|\cdot \|)=(\ell^2, \|\cdot \|_2)$. Let $e_n \in \ell^2$. Fora bounded linear functional $\phi$ on $X$, let $b_n=\phi (e_n)$ for each $n \geq 1$. Find the value of $p \geq 1$ such that the ...
68 views

Prove that a dual norm is of the same form as the norm in original vector space.

Let $\| \cdot \|$ be any norm on $E^n$. Define on $(E^n)^*$, the dual norm as follows. $$\| a \|^* = \max \{ a \cdot x: \lvert \lvert x \rvert \rvert = 1\}.$$ For every covector $a$, (a) Verify ...
I was reading about equivalent forms of the Kadison Singer Problem, and while looking at the Feichtinger Conjecture, I came across the claim that, for a projection operator $P$ and a self-adjoint ...
Let $V$ be a finite-dimensional Hilbert space and $G_k(V)$ the Grassmannian of $k$-dimensional subspaces of $V$. The $k$th exterior power $\bigwedge^k(V)$ can be equipped with a scalar product by ...