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More on convergence in unitary matrix spaces


Author: Jonathan Arazy
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
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Abstract: Let $ E$ be a symmetric sequence space satisfying the Radon-Riesz Property

$\displaystyle \{ \vert\vert{x_n}\vert\vert \to \vert\vert x\vert\vert{\text{and }}{x_n} \to x{\text{ weakly}}\} \Rightarrow \vert\vert{x_n} - x\vert\vert \to 0,$

then the same is true for the associated unitary matrix space $ C_{E}$.

References [Enhancements On Off] (What's this?)

  • [1] J. Arazy, Basic sequences, embeddings and the uniqueness of the symmetric structure in unitary matrix spaces, J. Funct. Anal. (to appear). MR 611587 (82g:47034)
  • [2] -, On the geometry of the unit ball of unitary matrix spaces, Integral Equations Operator Theory (to appear). MR 606129 (82g:46046)
  • [3] H. R. Grümm, Two theorems about $ {C_p}$, Rep. Math. Phys. 4 (1973), 211-215. MR 0327208 (48:5550)
  • [4] N. Tomczak-Jaegermann, The moduli of smoothness and convexity and Rademacher averages of trace classes $ {S_p}(1 \leqslant p < \infty )$, Studia Math. 50 (1974), 163-182. MR 0355667 (50:8141)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0619978-4
Keywords: Unitary matrix spaces, symmetric sequence spaces, compact operators on Hilbert space, Radon-Riesz Property
Article copyright: © Copyright 1981 American Mathematical Society

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