Mahesh Krishna, K.M.Johnson, P.S.Mohapatra, R.N.2026-02-042022Journal of Applied Mathematics and Informatics, 2022, 40, 46054, pp. 153-17127341194https://doi.org/10.14317/jami.2022.153https://idr.nitk.ac.in/handle/123456789/22786In 1960, Schatten studied operators of the form Σ∞ <inf>n=1</inf> λ<inf>n</inf>(x<inf>n</inf>⊗y<inf>n</inf>), where {x<inf>n</inf>}<inf>n</inf> and {y<inf>n</inf>}<inf>n</inf> are orthonormal sequences in a Hilbert space, and {λ<inf>n</inf>}<inf>n</inf> ∈ 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 Σ∞ <inf>n=1</inf> λ<inf>n</inf>(A∗ <inf>n</inf>x<inf>n</inf> ⊗ B∗ <inf>n</inf> y<inf>n</inf>), where {A<inf>n</inf>}<inf>n</inf> and {B<inf>n</inf>}<inf>n</inf> are operator-valued Bessel sequences, {x<inf>n</inf>}<inf>n</inf> and {y<inf>n</inf>}<inf>n</inf> are sequences in the Hilbert space such that {∥x<inf>n</inf>∥∥y<inf>n</inf>∥}<inf>n</inf> ∈ ℓ∞(ℕ). We also generalize the class of Hilbert-Schmidt operators studied by Balazs. © 2022 KSCAM.Hilbert-Schmidt classesMultipliersOperator-valued basesOperator-valued Bessel sequences