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}k∈N of H, a bijection αE: Bess(H) → L(H) can be defined. The aim of this paper is to characterize α-1 E (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.
@article{urn:eudml:doc:41871,
title = {Characterization of Bessel sequences.},
journal = {Extracta Mathematicae},
volume = {22},
year = {2007},
pages = {55-66},
zbl = {1161.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41871}
}
Arias, M. Laura; Corach, Gustavo; Pacheco, Miriam. Characterization of Bessel sequences.. Extracta Mathematicae, Tome 22 (2007) pp. 55-66. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41871/