• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.153-171
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• 2022

In 1960, Schatten studied operators of the form $\sum_{n=1}^{{\infty}}\;{\lambda}_n(x_n{\otimes}{\bar{y_n}})$, where {x_n}n and {y_n}_n are orthonormal sequences in a Hilbert space, and {λ_n}n ∈ ℓ^∞(ℕ). Balazs generalized some of the results of Schatten in 2007. In this paper, we further generalize results of Balazs by studying the operators of the form $\sum_{n=1}^{{\infty}}\;{\lambda}_n(A^*_nx_n{\otimes}{\bar{B^*_ny_n}})$, where {A_n}n and {B_n}_n are operator-valued Bessel sequences, {x_n}_n and {y_n}_n are sequences in the Hilbert space such that {║x_n║║y_n║}_n ∈ ℓ^∞(ℕ). We also generalize the class of Hilbert-Schmidt operators studied by Balazs.