Norm inequalities equivalent to Heinz inequality
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- by Junichi Fujii, Masatoshi Fujii, Takayuki Furuta and Ritsuo Nakamoto PDF
- Proc. Amer. Math. Soc. 118 (1993), 827-830 Request permission
Abstract:
We investigate several norm inequalities equivalent to the Heinz inequality and discuss the equivalence relations among these norm inequalities. Here we shall show an elementary and simplified proof to the famous Heinz inequality.References
- S. K. Berberian, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175–182. MR 107826, DOI 10.1090/S0002-9939-1959-0107826-9
- G. Corach, H. Porta, and L. Recht, An operator inequality, Linear Algebra Appl. 142 (1990), 153–158. MR 1077981, DOI 10.1016/0024-3795(90)90263-C
- Junichi Fujii and Masatoshi Fujii, A norm inequality for operator monotone functions, Math. Japon. 35 (1990), no. 2, 249–252. MR 1049088
- Takayuki Furuta, Norm inequalities equivalent to Löwner-Heinz theorem, Rev. Math. Phys. 1 (1989), no. 1, 135–137. MR 1041534, DOI 10.1142/S0129055X89000079
- Takayuki Furuta, $A\geq B\geq 0$ assures $(B^rA^pB^r)^{1/q}\geq B^{(p+2r)/q}$ for $r\geq 0$, $p\geq 0$, $q\geq 1$ with $(1+2r)q\geq p+2r$, Proc. Amer. Math. Soc. 101 (1987), no. 1, 85–88. MR 897075, DOI 10.1090/S0002-9939-1987-0897075-6
- Takayuki Furuta and Ritsuo Nakamoto, On the numerical range of an operator, Proc. Japan Acad. 47 (1971), 279–284. MR 291845
- Erhard Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann. 123 (1951), 415–438 (German). MR 44747, DOI 10.1007/BF02054965 A. McIntosh, Heinz inequalities and perturbation of spectral families, Macquarie Math. Reports, 1979.
- Gert K. Pedersen, Some operator monotone functions, Proc. Amer. Math. Soc. 36 (1972), 309–310. MR 306957, DOI 10.1090/S0002-9939-1972-0306957-4
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 827-830
- MSC: Primary 47A30; Secondary 47B15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1132412-1
- MathSciNet review: 1132412