Timeline for Topology on the set of analytic functions
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2019 at 2:57 | comment | added | Duchamp Gérard H. E. | I only corrected a small typo in yoour beautiful answer (+1) | |
| Oct 9, 2019 at 2:56 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
[unversal]--->[universal]
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| Mar 28, 2014 at 0:09 | comment | added | Alexandre Eremenko | @berlin: Thanks. Fortunately the book is available in our library:-) | |
| Mar 27, 2014 at 16:20 | comment | added | berlin | @Alexandre. More on the universal property of $H(U)'$. This was known to Fantappiè in 1943 (not in this language, of course)---see the concept of Fantappiè indicatrix of an operator--- and so before the Schwartzian theory of distributions and long before Grothendieck and Schwartz developed the connection between tensor products of lcs's and operators, in particular for nuclear spaces. A succinct discussion of this and the path from the original work of Fantappiè to its incorporation into modern function analysis by the actors mentioned above is in a review by Horvath, BAMS 25 (1991) p. 162 | |
| Mar 25, 2014 at 9:23 | history | edited | berlin | CC BY-SA 3.0 |
added a word
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| Mar 25, 2014 at 8:49 | history | edited | berlin | CC BY-SA 3.0 |
added 856 characters in body in reply to a comment
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| Mar 25, 2014 at 8:44 | history | edited | berlin | CC BY-SA 3.0 |
added 856 characters in body in reply to a comment
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| Mar 25, 2014 at 8:42 | comment | added | Jochen Wengenroth | The universal property of $E$ follows from Schwartz' $\varepsilon$-product (which in many cases coincides with the completed injective tensor product): $H(U,X) = H(U) \varepsilon X = L(H(U)'_{co}, X)$ where the last equality is the definition and $F'_{co}$ is the dual of the locally convex space $F$ endowed with uniform convergence on all absolutely convex compact sets. Since $H(U)$ is a Montel space, in our case this is the same as the strong dual of $H(U)$. | |
| Mar 25, 2014 at 8:30 | history | edited | berlin | CC BY-SA 3.0 |
added 856 characters in body
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| Mar 24, 2014 at 22:45 | comment | added | Alexandre Eremenko | berlin: could you give a more precise reference, for non-specialists on topological vector spaces, on the a) existence proof of such $E$ and b) that the dual of $H(U)$ has this property ? | |
| Mar 24, 2014 at 21:13 | history | answered | berlin | CC BY-SA 3.0 |