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5
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Second duals of Grothendieck spaces

The classical example of a Grothendieck space is $\ell_\infty$. It is also known that its even duals $\ell_\infty^{**}$, $\ell_\infty^{(4)}$, $\dots$ are Grothendieck spaces. (See, e.g., ...
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1answer
170 views

Are these ideals in rings of operators on Hilbert space unique?

Suppose that, for every Hilbert space $H$, we have a subset $I(H) \subseteq B(H)$ of bounded linear operators on $H$, and that together all $I(H)$ form a two-sided ideal, in the sense that whenever $h ...
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2answers
338 views

Factorization through $\ell_{1}$ and operator ideals

Recently, I bumped into the class of operators that factor through $\ell_{1}(X)$ for some set $X$. For now, $X$ is a set with arbitrary cardinality but if it leads to a more concrete answer to my ...