\(g\)-Bessel Sequences and Operators - Khosravi, Amir; Takhteh, Farkhondeh (Communications in Mathematics and Applications, 2016)
Let $H$ be a separable Hilbert space, and let \(g\mathfrak{B}\) be the set of all \(g\)-Bessel sequences for \(H\). We show that \(g\mathfrak{B}\) is a \(C^*\)-algebra isometrically isomorphic to \(L(H)\) (the algebra of all bounded linear operators of \(H\)). Also, we classify \(g\)-Bessel sequences in \(H\) in terms of different kinds of operators in \(L(H)\). Using operator theory tools, we investigate geometry of \(g\)-Bessel sequences.
Keywords: g-Bessel sequence; g-Orthonormal basis; g-Riesz basis; Bounded linear operator