Another generalization of Anderson’s theorem
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- by Hong Ke Du PDF
- Proc. Amer. Math. Soc. 123 (1995), 2709-2714 Request permission
Abstract:
In this paper, we prove that if A and B are normal operators on a Hilbert space H, then, for every operator S satisfying $ASB = S, \left \| {AXB - X + S} \right \| \geq {\left \| A \right \|^{ - 1}}{\left \| B \right \|^{ - 1}}\left \| S \right \|$ for all operators $X \in B(H)$, and that if A and B are contractions, then, for every operator S satisfying $ASB = S$ and ${A^ \ast }S{B^ \ast } = S,\left \| {AXB - X + S} \right \| \geq \left \| S \right \|$ for all operators $X \in B(H)$, where $B(H)$ denotes the set of all bounded linear operators on H.References
- Joel Anderson, On normal derivations, Proc. Amer. Math. Soc. 38 (1973), 135–140. MR 312313, DOI 10.1090/S0002-9939-1973-0312313-6 Du Hong-ke and Xu Wangtao, Generalizations of Anderson’s theorem and Maher’s theorem, Pure Appl. Math. 9 (1993), 35-41.
- B. P. Duggal, A remark on normal derivations of Hilbert-Schmidt type, Monatsh. Math. 112 (1991), no. 4, 265–270. MR 1141094, DOI 10.1007/BF01351767
- P. J. Maher, Commutator approximants, Proc. Amer. Math. Soc. 115 (1992), no. 4, 995–1000. MR 1086335, DOI 10.1090/S0002-9939-1992-1086335-6
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2709-2714
- MSC: Primary 47B15; Secondary 47A30, 47A63, 47B47
- DOI: https://doi.org/10.1090/S0002-9939-1995-1273496-1
- MathSciNet review: 1273496