Dual space of KC

[Micael]

Dear all!

I am wondering if anything is known about the dual space of the
space of all functions $f: [0,1]\to R$, that have finite one-sided
limits in every point, endowed with $sup$-norm?
More exactly, let $M$ be the space of functions satisfying $f(x)=1/2
(f
(x+0)+f(x-0))$ at any $x\in (0,1)$ and $f(0+)=f(0)$, $f(1-)=f(1)$ with
$sup$-norm. Is there any description for $M*$?

Or, maybe, for the space of piecewise continuous functions on $[0,1]$?

I'd appreciate any reference/information!

Sincerely,
Michael.

[G. A. Edgar]

In article
<da5378f2-37e2-4d62...@v25g2000yqk.googlegroups.com>,
Micael <music...@gmail.com> wrote:

> Dear all!
>
> I am wondering if anything is known about the dual space of the
> space of all functions $f: [0,1]\to R$, that have finite one-sided
> limits in every point, endowed with $sup$-norm?
> More exactly, let $M$ be the space of functions satisfying $f(x)=1/2
> (f
> (x+0)+f(x-0))$ at any $x\in (0,1)$ and $f(0+)=f(0)$, $f(1-)=f(1)$ with
> $sup$-norm. Is there any description for $M*$?

Consider this space to be C(K), where K is the two-arrows space.
(top and bottom of the lexicographic square, Sorgenfrey interval).
Since K is compact Hausdorff, the dual is M(K), the space of
signed measures on K.

>
> Or, maybe, for the space of piecewise continuous functions on $[0,1]$?
>
> I'd appreciate any reference/information!
>
> Sincerely,
> Michael.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

[Micael]

On 10 նոյ, 14:17, "G. A. Edgar" <ed...@math.ohio-state.edu.invalid>
wrote:
> In article
> <da5378f2-37e2-4d62-8f4f-cae1dfc37...@v25g2000yqk.googlegroups.com>,

Thanks a lot!!!

Michael.