Abstract
The main result is that the cluster value problem in separable Banach spaces, for the Banach algebras $A_{u}$ and $H^{\infty}$, can be reduced to the cluster value problem in those spaces which are $\ell_{1}$ sums of a sequence of finite dimensional spaces. In particular, we prove that the cluster value problem for $\ell_{1}$ is equivalent to the cluster value problem for $L_{1}(0,1)$.
Citation
W. B. Johnson. S. Ortega Castillo. "The cluster value problem for Banach spaces." Illinois J. Math. 58 (2) 405 - 412, Summer 2014. https://doi.org/10.1215/ijm/1436275491
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