Removing a space from file name

I have several hundred *.jpg files with this pattern

Actual example:

   'AtlantaVisitAndGrandmaHands 056.jpg'

The numbers vary, of course, but the alpha part and number of digits
after the space is the same in all *.jpg files

I have hundreds of these all in one directory.  Not something you'd
want to do one at a time.

I tried to figure a way using the perl `rename' tool found in many linux
distro's repos

But couldnt figure out the necessary syntax from Larry Wall's examples
in the rename man page.  Using the "s///" operators ,  it's probably
there some how but my pea brain isn't seeimg it.

bash has just used the apostrophes to make the names usable but
I would much rather remove the space.