Characterization of Bessel sequences

M. L. ARIAS, G. CORACH, M. PACHECO

Extracta Mathematicae

Universidad de Extremadura- Departamento de matemática

Año: 2007 vol. 22 p. 55 - 66

0213-8743

Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and Bess(H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {ek} of H, a bijection T :Bess(H) − L(H) can be defined. The aim of this paper is to characterize T−1 (A) for different classes of operators A  of L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and Bess(H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {ek} of H, a bijection T :Bess(H) − L(H) can be defined. The aim of this paper is to characterize T−1 (A) for different classes of operators A  of L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.