SONGKLANAKARIN JOURNAL OF SCIENCE & TECHNOLOGY

Volume 41, No. 04, Month JULY, Year 2019, Pages 727 - 733

Algebraic, order, and analytic properties of tracy-singh sums for hilbert space operators

Arnon Ploymukda and Pattrawut Chansangiam

Abstract Download PDF

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

Keywords

operator matrix, tensor product, Tracy-Singh product, Tracy-Singh sum, analytic functions of operators

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