# Tagged Questions

**-4**

votes

**1**answer

149 views

### Is there always a subspace of $L^p$ isomorphic to direct sums of $\ell^2,\ell^p$? [closed]

It is known that each $L^p$ (on a space with finite measure like $[0,1]$) $p>1$ space contains an isomorphic complemented copy of $\ell^2$ and $\ell^p$. I think this is the Kadets-Pelczynski ...

**1**

vote

**0**answers

102 views

### Relationship between weak Lp and strong Lq topologies for q<p

Specificaly:
Does convergence in $L^{\frac{1}{2}}$ imply weak $L^2$ convergence?
Having a limit in $L^{\frac{1}{2}}$ topology and a limit in weak $L^2$ topology whether these are always equal? If ...

**3**

votes

**0**answers

104 views

### trace-class embeddings

There is a classical theorem of Riesz-Kolmogorov that characterizes compact embedding in $L^p$-spaces of some subspace of them. A generalization to arbitrary metric spaces has been recently obtained ...