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Algebraic, order, and analytic properties of Tracy-Singh sums for Hilbert space operators
Author(s)
Ploymukda, Arnon
Date Issued
July 1, 2019
Type
Article
Abstract
We introduce the Tracy-Singh sum for operators on a Hilbert space, generalizing both the Tracy-Singh sum for matrices and the tensor sum for operators. The Tracy-Singh sum is shown to be compatible with algebraic operations and order relations. Then we establish a binomial theorem involving Tracy-Singh sums, and its consequences. We also investigate continuity, convergence, and norm bounds for Tracy-Singh sums. Moreover, we derive operator identities involving Tracy-Singh sums and certain operator functions defined by power series.
Citation
Songklanakarin Journal of Science and Technology, 41(4), 727-733, 2019