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MULTIPLIERS FOR OPERATOR-VALUED BESSEL SEQUENCES AND GENERALIZED HILBERT-SCHMIDT CLASSES
(Korean Society for Computational and Applied Mathematics, 2022) Mahesh Krishna, K.M.; Johnson, P.S.; Mohapatra, R.N.
In 1960, Schatten studied operators of the form Σ∞ n=1 λn(xn⊗yn), where {xn}n and {yn}n are orthonormal sequences in a Hilbert space, and {λn}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 Σ∞ n=1 λn(A∗ nxn ⊗ B∗ n yn), where {An}n and {Bn}n are operator-valued Bessel sequences, {xn}n and {yn}n are sequences in the Hilbert space such that {∥xn∥∥yn∥}n ∈ ℓ∞(ℕ). We also generalize the class of Hilbert-Schmidt operators studied by Balazs. © 2022 KSCAM.