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Algebraic, order, and analytic properties of Tracy-Singh sums for Hilbert space operators |
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| รหัสดีโอไอ | |
| Creator | 1. Arnon Ploymukda 2. Pattrawut Chansangiam |
| Title | Algebraic, order, and analytic properties of Tracy-Singh sums for Hilbert space operators |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2019 |
| Journal Title | Songklanakarin Journal of Science and Technology |
| Journal Vol. | 41 |
| Journal No. | 4 |
| Page no. | 727-733 |
| Keyword | operator matrix, tensor product, Tracy-Singh product, Tracy-Singh sum, analytic functions of operators |
| URL Website | http://rdo.psu.ac.th/sjstweb/index.php |
| ISSN | 0125-3395 |
| 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. |
