p. 159 - 164 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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2013, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |