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Is there any criterion answering the question:

Let $E$ be a Banach space. When does the Banach space $\mathcal{B}(E)$ of all bounded operators on $E$ contain a copy of $\ell^\infty(\Gamma)$? Here $\Gamma$ is an arbitrary index set, perhaps uncountable.

Of course, the answer is easy when $E$ is a Hilbert space with density character equal to the cardinality of $\Gamma$.

Thank you.

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    A sufficient condition would be the existence of a complemented subspace with an unconditional basis. On that subspace, then, you can just copy the argument that works for a Hilbert space. I don't know whether that is necessary, though. I think the [Argyros-Haydon](http://arxiv.org/abs/0903.3921) space has a separable space of bounded linear operators, so some supplementary information is necessary.2011-10-08
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    Of course, but I am pretty sure that some time ago I've seen a paper precisely on that matter. Unfortunately, browsing mathscinet gives me nothing...2011-10-08
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    Was it by any chance [this paper](http://www.math.sc.edu/~giorgis/embeddingellinfty.pdf)? Here's its [MathSciNet review](http://www.ams.org/mathscinet-getitem?mr=2285251).2011-10-08
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    You are superb! Thank you, thanks a lot!2011-10-08
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    You're welcome :) I didn't know it, I just Googled for `embedding l^\infty into bounded operators` and it was one of the first hits.2011-10-08
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    My problem was that I was not sure how to type l^\infty into mathscinet/google :)2011-10-08
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    What is $\Gamma$?2011-10-08
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    Any index set, perhaps uncountable.2011-10-08
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    It would be helpful for readers to include this in the body of the question.2011-10-08

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