You didn't show the output you desire, so I can only guess, but I would try an approach like this:

use strict;
use warnings;
use Date::Manip;

my %owners;
while (<DATA>) {
    my ($mode, $owner, $job_id, $timestamp) = (split)[0..2,7];
    next unless $owner =~ /oracle|sybase/;
    $owners{$owner}{$job_id}{$mode} = $timestamp;
}

for my $owner (keys %owners) {
    for my $job (keys %{ $owners{$owner} }) {
        if (exists $owners{$owner}{$job}{'>'}) {
            my $t1 = $owners{$owner}{$job}{'<'};
            my $t2 = $owners{$owner}{$job}{'>'};
            my $d = DateCalc($t2, $t1);
            print "$owner - JobID:$job - RunTime:$d\n";
        }
    }
}

__DATA__
<  root 26144 c Tue Nov  2 03:10:02 2010
<  oracle 26161 c Tue Nov  2 03:10:25 2010  
<  oracle 26193 c Tue Nov  2 03:10:30 2010
<  sybase 26163 c Tue Nov  2 03:10:32 2010
>  oracle 26161 c Tue Nov  2 03:10:33 2010
<  sybase 26188 c Tue Nov  2 03:10:38 2010
>  sybase 26163 c Tue Nov  2 03:10:58 2010
[download]

Prints out:

oracle - JobID:26161 - RunTime:-0:0:0:0:0:0:8
sybase - JobID:26163 - RunTime:-0:0:0:0:0:0:26
[download]