ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE





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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Acta Mathematica Universitatis Comenianae
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