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- W2896768151 abstract "We obtain a description of all pairs of Hermitian operators X and Y, which satisfy the condition −Y ≤ X ≤ Y. We give the examples of such operator pairs. Each of the presented examples leads us to the new weak majorization for the Hermitian operator pair. It is shown that this inequality does not necessarily imply the inequality |X| ≤ ZY Z* for any operator Z, ‖Z‖ ≤ 1. We prove that invertibility of Y follows from invertibility of operators X and A* A for Hermitian operators X and Y, Y ≥ 0 and an arbitrary operator A such that −AY A* ≤ X ≤ AY A*. We discuss one analog of triangle inequality found by the author in one earlier paper for pairs of Hermitian operators." @default.
- W2896768151 created "2018-10-26" @default.
- W2896768151 creator A5016047074 @default.
- W2896768151 date "2013-01-01" @default.
- W2896768151 modified "2023-09-26" @default.
- W2896768151 title "On hermitian operators X and Y meeting the condition -Y ≤ X ≤ Y" @default.
- W2896768151 hasPublicationYear "2013" @default.
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