On Stability of Bases in Hilbert Spaces - Larionov, Evgeny (Eurasian Mathematical Journal, 2020)
In a Hilbert space we consider a minimal and complete system asymptotically close to an almost normed unconditional basis and find conditions under which such system also forms an unconditional basis. The proof of this statement is based on a new criterion of compactness of linear operators proposed in this paper.