# Uniqueness up to isometric isomorphism of predual of $(\sum_{\lambda\in\Lambda} H_\lambda)_{l_\infty}$ where $H_\lambda$ are Hilbert spaces

This fact is an easy consequence of results of the paper by Leon Brown and Takashi Ito, but it looks like an overkill. Does anyone know a simpler proof?

• For this particular space you can play the same game as in Example 2.1 here: math.uchicago.edu/~amwright/DavidsonWright2.pdf Aug 9 '13 at 11:20
• @TomekKania I think you can post this as answer Aug 9 '13 at 16:15