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Some inequalities for commutators and an application to spectral variation. II |
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| Authors: | Rajendra Bhatia Fuad Kittaneh Ren Cang Li |
| Institution: | a Indian Statistical Institute, New Delhi, India b Department of Mathematics, University of Jordan, Amman, Jordan c Mathematical Science Section, Oak Ridge National Laboratory, Oak Ridge, TN |
| Abstract: | Inequalities that compare unitarily invariant norms of A - B and those of AΓ - ΓB and Γ-1A - B Γ-1 are obtained, where both A and B are either Hermitian or unitary or normal operators and Γ is a positive definite operator in a complex separable Hilbert space. These inequalities are then applied to derive bounds for spectral variation of diagonalisable matrices. Our new bounds improve substantially previously published bounds. |
| Keywords: | Linear operator commutator unitarily invariant norm diagonalisable matrix spectral variation AMS Subject Classification: 15A42 15A60 65F99 |
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