This fact is an easy consequence of results of the paper Classes of Banach spaces with unique isometric preduals. by Leon Brown and Takashi Ito, but it looks like an overkill. Does anyone know a simpler proof?
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$\begingroup$ For this particular space you can play the same game as in Example 2.1 here: math.uchicago.edu/~amwright/DavidsonWright2.pdf $\endgroup$– Tomasz KaniaCommented Aug 9, 2013 at 11:20
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$\begingroup$ @TomekKania I think you can post this as answer $\endgroup$– NorbertCommented Aug 9, 2013 at 16:15
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1 Answer
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In this particular case, you can proceed similarly as in Example 2.1 here. For more general results please consult a fantastic survey on unique preduals by G. Godefroy:
G. Godefroy. Existence and uniqueness of isometric preduals: a survey. In: BorLuh Lin, editor, Banach Space Theory. Proc. of the Iowa Workshop on Banach Space Theory 1987, 131–193. Contemp. Math. 85, 1989.
answered Aug 9, 2013 at 17:13
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$\begingroup$ do you have electronic copy of this survey. Neither I, nor my institute don't have access to Contemporary Mathematics. $\endgroup$– NorbertCommented Jan 31, 2014 at 12:58
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$\begingroup$ Norbert, the whole paper is fully available (at least to me) through google books: books.google.co.uk/… $\endgroup$ Commented Jan 31, 2014 at 18:23
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1$\begingroup$ unfortunately it is not fully avaliable for me even via your link $\endgroup$– NorbertCommented Jan 31, 2014 at 20:40