Carl's inequality for quasi-Banach spaces

Aicke Hinrichs, Anton Kolleck, Jan Vybiral

We prove that for any two quasi-Banach spaces $X$ and $Y$ and any $\alpha >0$ there exists a constant ${\gamma }_{\alpha }>0$ such that $$ \sup_{1\le k\le n}k^αe_k(T)\le γ_α\sup_{1\le k\le n} k^αc_k(T)…