More on convergence in unitary matrix spaces
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- by Jonathan Arazy
- Proc. Amer. Math. Soc. 83 (1981), 44-48
- DOI: https://doi.org/10.1090/S0002-9939-1981-0619978-4
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Abstract:
Let $E$ be a symmetric sequence space satisfying the Radon-Riesz Property \[ \{ ||{x_n}|| \to ||x||{\text {and }}{x_n} \to x{\text { weakly}}\} \Rightarrow ||{x_n} - x|| \to 0,\] then the same is true for the associated unitary matrix space $C_{E}$.References
- Jonathan Arazy, Basic sequences, embeddings, and the uniqueness of the symmetric structure in unitary matrix spaces, J. Functional Analysis 40 (1981), no.Β 3, 302β340. MR 611587, DOI 10.1016/0022-1236(81)90052-5
- Jonathan Arazy, On the geometry of the unit ball of unitary matrix spaces, Integral Equations Operator Theory 4 (1981), no.Β 2, 151β171. MR 606129, DOI 10.1007/BF01702378
- H. R. GrΓΌmm, Two theorems about ${\scr C}_{p}$, Rep. Mathematical Phys. 4 (1973), 211β215. MR 327208, DOI 10.1016/0034-4877(73)90026-8
- Nicole Tomczak-Jaegermann, The moduli of smoothness and convexity and the Rademacher averages of trace classes $S_{p}(1\leq p<\infty )$, Studia Math. 50 (1974), 163β182. MR 355667
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 44-48
- MSC: Primary 46A45; Secondary 46B20, 47D45
- DOI: https://doi.org/10.1090/S0002-9939-1981-0619978-4
- MathSciNet review: 619978