Complex strict and uniform convexity and hyponormal operators. (English) Zbl 0558.47020
A report of this paper [Rep., Dept. Math., Univ. Stockholm 15 (1983)] was reviewed in Zbl 0516.47014. One of the main results in the report was that the trace class is uniformly c-convex. In the present paper the proof of this theorem is improved by improving the preceding inequality for trace class operators. In addition some smaller changes have been made in the report. A more general result of U. Haagerup on the convexity of the dual space of a \(C^*\)-algebra has appeared in the paper of W. J. Davis, D. J. H. Garling and N. Tomczak-Jaegermann [J. Funct. Anal. 55, 110-150 (1984)].
MSC:
| 47B20 | Subnormal operators, hyponormal operators, etc. |
| 47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |
| 47L07 | Convex sets and cones of operators |
| 47B47 | Commutators, derivations, elementary operators, etc. |
| 47A12 | Numerical range, numerical radius |
Citations:
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