Timeline for A characterization of nuclear functionals in terms of continuity with respect to some special topologies on $B(X)$?
Current License: CC BY-SA 4.0
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| Apr 12, 2019 at 18:49 | comment | added | Sergei Akbarov | @MeisamSoleimaniMalekan why if a functional $\varphi$ is continuous on compact sets of $L(X,Y)$ then it is continuous on $L(X,Y)$ (where $L(X,Y)$ is endowed with the compact-open topology)? | |
| Apr 12, 2019 at 18:05 | comment | added | MSMalekan | Proposition 1.e.3 in "J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, I, Springer Verlag, Classics in Mathematics, 1996." I think is what you want. | |
| Apr 12, 2019 at 17:05 | comment | added | Sergei Akbarov | @BillJohnson could you, please, give a more precise reference? Which statement in Lindenstrauss-Tzafriri do you mean? | |
| Apr 12, 2019 at 16:24 | comment | added | Bill Johnson | Your conjecture is correct. This is covered in volume one of Lindenstrauss-Tzafriri. Tricky things happen when X fails the approximation property (one must distinguish nuclear operators from nuclear tensors), but that is also treated in Lindenstrauss-Tzafriri. X has the AP if and only if trace is well defined for nuclear operators. That is, if X fails the AP, then there is a nuclear representation of the zero operator for which the trace of the representation can be anything. | |
| Apr 12, 2019 at 14:37 | history | edited | Sergei Akbarov | CC BY-SA 4.0 |
added 49 characters in body
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| Apr 12, 2019 at 14:29 | history | asked | Sergei Akbarov | CC BY-SA 4.0 |