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http://dx.doi.org/10.14317/jami.2022.153

MULTIPLIERS FOR OPERATOR-VALUED BESSEL SEQUENCES AND GENERALIZED HILBERT-SCHMIDT CLASSES  

KRISHNA, K. MAHESH (Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka(NITK))
JOHNSON, P. SAM (Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka(NITK))
MOHAPATRA, R.N. (Department of Mathematics, University of Central Florida)
Publication Information
Journal of applied mathematics & informatics / v.40, no.1_2, 2022 , pp. 153-171 More about this Journal
Abstract
In 1960, Schatten studied operators of the form $\sum_{n=1}^{{\infty}}\;{\lambda}_n(x_n{\otimes}{\bar{y_n}})$, 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 $\sum_{n=1}^{{\infty}}\;{\lambda}_n(A^*_nx_n{\otimes}{\bar{B^*_ny_n}})$, 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.
Keywords
Multipliers; operator-valued bases; operator-valued Bessel sequences; Hilbert-Schmidt classes;
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