2 problems

Let ${\cal H}$ be a Hilbert space. A sequence $(f_n)$ in ${\cal H}$ is a weighted frame when there exists $(\omega_n)\subset(0,+\infty)$ such that $(\omega_n f_n)$ is a frame for…

Schauder–Badea conjecture. The series converges unconditionally for every $x \in H$ if and only if there exist scalar sequences $(c_n)_{n \in \mathbb{N}}$ and…