  The scalar-isoscalar pi-pi phase shifts are calculated in the pi-pi energy
range from 600 MeV to 1600 MeV. We use results of the CERN-Cracow-Munich
collaboration for the reaction pi^- p --> pi^+ pi^- n on a transversely
polarized target at 17.2 GeV/c pi^- momentum. Energy-independent separation of
the S-wave pseudoscalar amplitude (pi exchange) from the pseudovector amplitude
(a_1 exchange) is carried out. Below the KK threshold we find two solutions for
the pi-pi phase shifts, for which the phases increase slower with the effective
pi-pi mass than the P-wave phases ("flat" solutions) and two solutions for
which the phases increase faster than the P-wave phases ("steep" solutions).
Above 1420 MeV both sets of phase shifts increase with energy faster than in
the experiment on an unpolarized target. This fact can be related to a presence
of the scalar resonance f_0(1500).
