Timeline for Bochner integrals with values in a Hilbert $A$-module
Current License: CC BY-SA 3.0
8 events
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| Dec 7, 2017 at 16:29 | comment | added | geometricK | Thanks Corbennick and t.c. for the nice references. Now I'm reasonably convinced that Bochner integration theory gives the property in the second equality. I just have to make sense of some integrals with values in a (non-separable) C*-algebra...math.stackexchange.com/questions/2555677/… | |
| Dec 7, 2017 at 9:40 | comment | added | user85913 | Theorem C.12 in Raeburn-Williams's book "Morita equivalence and continuous-trace $C^*$-algebras" might be relevant to this question. | |
| Dec 7, 2017 at 7:24 | comment | added | user1688 | Bochner integrals exist for functions with values in any locally convex space, see arxiv.org/pdf/1403.3207.pdf | |
| Dec 6, 2017 at 15:58 | comment | added | geometricK | Yes, but I don't know whether the direct analogue of the usual Bochner integral makes sense for Hilbert module-valued functions. I can see that uniqueness is guaranteed once existence is proved. Perhaps it would be more accurate to refer to this as a Gelfand-Pettis integral rather than a Bochner integral... | |
| Dec 6, 2017 at 8:25 | comment | added | user1688 | The usual Bochner integral has the property that it commutes with every continuous linear map. | |
| Dec 6, 2017 at 6:33 | comment | added | geometricK | But the inner product in the second equality takes values in $A$, right? | |
| Dec 6, 2017 at 6:00 | comment | added | user1688 | What is the difference between the first and the second statement? Since the $A$-module structure does not appear in the statement, it seems obviously true. | |
| Dec 6, 2017 at 5:54 | history | asked | geometricK | CC BY-SA 3.0 |