Timeline for Do all $L^{\infty}(\mu)$ spaces have the Grothendieck property?
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| Apr 14, 2014 at 3:10 | comment | added | Tomasz Kania | user46855, you should post that as the answer. | |
| Mar 31, 2014 at 20:48 | comment | added | user46855 | Since the Encyclopedia of Mathematics is not explicit in the references for $L^\infty$, consider this: a generic $L^\infty$ as vector lattice of self-adjoint elements is Dedekind $\sigma$-complete (and complete iff localizable); its spectrum as $C^*$-algebra is then $\sigma$-stonean (see Berberian, Baer$^*$ rings, page 45 or Meyer-Nieberg, Banach lattices, page 54) and now see Ando or Seever cited by the Encyclopedia. | |
| Mar 26, 2014 at 17:34 | comment | added | UwF | The Encyclopedia of Mathematics lists $L_\infty(\mu)$ as examples of Grothendieck spaces, without any conditions. I guess you should check the references they cite, see encyclopediaofmath.org/…. | |
| Mar 26, 2014 at 15:52 | history | edited | user44155 | CC BY-SA 3.0 |
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| Mar 26, 2014 at 14:16 | history | edited | user5810 | CC BY-SA 3.0 |
copy-editing
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| Mar 26, 2014 at 11:57 | history | asked | user44155 | CC BY-SA 3.0 |