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Analytic properties of tracy-singh products for operator matrices
Author(s)
Date Issued
January 1, 2018
Type
Article
Abstract
We show that the Tracy-Singh product of Hilbert space operators is continuous with respect to the operator-norm topology. The Tracy-Singh product of two nonzero operators is compact if and only if both factors are compact. We provide upper and lower bounds for certain Schatten p-norms of the Tracy-Singh product of operators. It turns out that this product is continuous with respect to the topologies on norm ideals of compact operators, trace class operators, and Hilbert-Schmidt class operators. Thus the Tracy-Singh product preserves such classes of operators.
Citation
Journal of Computational Analysis and Applications, 24(4), 665-674, 2018