\(g\)-bases in Hilbert spaces
Summary: The concept of \(g\)-bases in Hilbert spaces is introduced, which generalizes Schauder bases in Hilbert spaces. Some results about \(g\)-bases are proved. In particular, we characterize the \(g\)-bases and \(g\)-orthonormal bases. Dual \(g\)-bases are also discussed. We also consider the equivalent relations of \(g\)-bases and \(g\)-orthonormal bases. The property of \(g\)-minimality of \(g\)-bases is studied as well. Our results show that, in some cases, \(g\)-bases share many useful properties of Schauder bases in Hilbert spaces.
scientific article; zbMATH DE number 6134194
scientific article