Norm estimations, continuity, and compactness for Khatri-Rao products of Hilbert Space operators
| Autor: | Pattrawut Chansangiam, Arnon Ploymukda |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
General Mathematics Trace norm Hilbert space General Physics and Astronomy General Chemistry Schatten class operator Compact operator Computer Science::Numerical Analysis General Biochemistry Genetics and Molecular Biology symbols.namesake Compact space If and only if Norm (mathematics) symbols General Agricultural and Biological Sciences Operator norm Mathematics |
| Zdroj: | Malaysian Journal of Fundamental and Applied Sciences. 14:382-386 |
| ISSN: | 2289-599X 2289-5981 |
| DOI: | 10.11113/mjfas.v14n4.881 |
| Popis: | We provide estimations for the operator norm, the trace norm, and the Hilbert-Schmidt norm for Khatri-Rao products of Hilbert space operators. It follows that the Khatri-Rao product is continuous on norm ideals of compact operators equipped with the topologies induced by such norms. Moreover, if two operators are represented by block matrices in which each block is nonzero, then their Khatri-Rao product is compact if and only if both operators are compact. The Khatri-Rao product of two operators are trace-class (Hilbert-Schmidt class) if and only if each factor is trace-class (Hilbert-Schmidt class, respectively). |
| Databáze: | OpenAIRE |
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