\(g\)-Bessel Sequences and Operators

Amir Khosravi, Farkhondeh Takhteh

Abstract


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

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DOI: http://dx.doi.org/10.26713%2Fcma.v7i2.398

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