Try:

Max @ A[[All, #]] & /@ Range[4]

Which gives:

{0.474042, 0.50765, 0.4977, 0.539773}

A = { {0.474042,0.507508,0.4977,0.539773},  {0.473447,0.50765,0.483809,0.52489},
     {0.46797,0.483669,0.494823,0.516956}, {0.467079,0.483509,0.478704,0.501286}}

Try

Max @ A[[All, #]] & /@ Range[4]

Which gives:

{0.474042, 0.50765, 0.4977, 0.539773}

You can also do:

Max @@@ (A\[Transpose])