  Magnetization and muon spin rotation experiments were performed in
La_(2-x)Ba_xCuO_4 (x = 1/8) as a function of hydrostatic pressure up to p = 2.2
GPa. It was found that the magnetic volume fraction of the static stripe phase
strongly decreases linearly with pressure, while the superconducting volume
fraction increases by the same amount. This demonstrates competition between
bulk superconductivity and static magnetic order in the stripe phase of
La_1.875Ba_0.125CuO_4 and that these phenomena occur in mutually exclusive
spatial regions. The present results also reveal that the static spin-stripe
phase still exists at pressures, where the long-range low-temperature
tetragonal (LTT) structure is completely suppressed. This indicates that the
long-range LTT structure is not necessary for stabilizing the static spin order
in La_1.875Ba_0.125CuO_4.
