Two classes of \(J\)-operators. (English) Zbl 1538.47035
Summary: We define two classes \({\mathfrak{A}}\) and \({\mathfrak{B}}\) in the space \({\mathcal{B}}({\mathcal{H}})\) of operators acting on a Hilbert space on the basis of \(J\)-order relation and spectra, and discuss various properties related to these classes.
MSC:
| 47B02 | Operators on Hilbert spaces (general) |
| 46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
| 47A64 | Operator means involving linear operators, shorted linear operators, etc. |
| 15A45 | Miscellaneous inequalities involving matrices |
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