# Tag: banach-spaces

## reference request – Continuous projections on $\ell_1$ with norm $>1$

The Question : 119 people think this question is useful I was trying to find papers and articles about non-contractive continuous projections on $\ell_1(S)$ where $S$ is an arbitrary set. If it is not studied yet, I would like to know results for the case $S=\mathbb{N}$. I’ve found one quite general condition for the closed

## real analysis – Is it possible for a function to be in $L^p$ for only one $p$?

The Question : 125 people think this question is useful I’m wondering if it’s possible for a function to be an $L^p$ space for only one value of $p \in [1,\infty)$ (on either a bounded domain or an unbounded domain). One can use interpolation to show that if a function is in two $L^p$ spaces,

## functional analysis – Does the open mapping theorem imply the Baire category theorem?

The Question : 220 people think this question is useful A nice observation by C.E. Blair1, 2, 3 shows that the Baire category theorem for complete metric spaces is equivalent to the axiom of (countable) dependent choice. On the other hand, the three classical consequences of the Baire category theorem in basic functional analysis — the