On dual of Banach sequence spaces
A. A. Ledari and V. Parvaneh
Received: May 28, 2012; Revised: December 28, 2012; Accepted: March 7, 2013
Abstract. J. Hagler and P. Azimi have introduced a class of Banach sequence spaces, the Xα,1 spaces as a class of hereditarily $\ell_1$ Banach spaces. In this paper, (i) We show that X*α, 1, the dual of Banach space Xα,1 contains asymptotically isometric copies of $\ell_\infty$. (ii) With two methods, we show that X*α,1 is nonseparable although Xα,1 is a separable Banach space. Also, we show Xα,1 is not hereditarily indecomposable.
Keywords: Banach spaces; asymptotically isometric copies; nonseparable dual.
AMS Subject classification: Primary: 46B04 Secondary: 46B20
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