Timeline for Dual of the space of all bounded functions, $B(X, \mathbb{R}).$
Current License: CC BY-SA 3.0
5 events
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| Mar 20, 2017 at 23:12 | comment | added | user95282 | For Question 2: Every $f\in C(K,\mathbb{R})$ extends to a function in $C_b(X,\mathbb{R})$. So $\mathcal{M}(K)$ embeds into $(C_b(X,\mathbb{R})^\ast$ in a natural way. | |
| Mar 20, 2017 at 22:41 | comment | added | Nate Eldredge | The canonical place to look is Dunford and Schwartz. | |
| Mar 20, 2017 at 22:12 | history | edited | Eduardo | CC BY-SA 3.0 |
added 4 characters in body
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| Mar 20, 2017 at 22:02 | comment | added | Tomasz Kania | $C_b(X)^*\cong M(\beta X)$, $B(X)^*\cong M(\beta X_d)$, where $X_d$ is $X$ endowed with the discrete topology. As for your second question you have only a surjection from one of the latter spaces onto $C(K)^*$. | |
| Mar 20, 2017 at 21:57 | history | asked | Eduardo | CC BY-SA 3.0 |