Timeline for Separable von Neumann algebra
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 15, 2016 at 21:13 | comment | added | oeiras | Let me add some context to the above method. There are many examples of Banach spaces (of bounded continuous, analytic, measurable,..., functions and of operators) with supremum norm and these are, in general, not separable, more precisely, there are results analogous to the one above, namely that separability only occurs under very special conditions. Thus a commutative $C^\star$-algebra with unit is separable iff it is $C(K)$ with $K$ compact, metrisable. The above CGT gives a unified explanation of this fact since these spaces have analogous weaker topologies for which it applies. | |
| Mar 15, 2016 at 19:20 | comment | added | oeiras | That a functional thereon is ultraweakly continuous if its restriction to each commutative subalgebra has the same property. | |
| Mar 15, 2016 at 17:37 | comment | added | Nik Weaver | "Standard facts on von Neumann algebras"? | |
| Mar 15, 2016 at 15:52 | comment | added | oeiras | The commutative case is covered on p. 167 of the book "Saks spaces and applications to functional analysis" which is available online, the reduction to the commutative case follows from standards facts on von Neumann algebras. | |
| Mar 15, 2016 at 14:49 | comment | added | Simon Henry | Do you know a reference for this closed graph theorem results ? | |
| Mar 15, 2016 at 14:26 | history | answered | oeiras | CC BY-SA 3.0 |