We will discuss two recent groups of results related to frame theory. The first group, which is joint work with Pu-Ting Yu, focuses on convergence of alternative duals for frames. We know that a frame has a canonical dual frame, and that frame series converge unconditionally when we use the canonical dual. What happens when we use alternative duals, can we have unconditional convergence? Always have unconditional convergence? We will discuss these questions and address the excess of alternative duals. The second group, which is joint work with Logan Hart, Ian Katz, and Michael Northington, focuses on issues related to summability of frame coefficients. We discuss the idea of $\ell^1$-bounded set introduced by Haak and Haase and the corresponding notion for frames. Several open problems will be identified, some of which have intriguing implications.
https://univienna.zoom.us/j/67922750549?pwd=Ulh5L1QxNFhBOC9PUjlVdG9hc0tmUT09