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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}$.

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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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