Motivated by recent works on spectrum-sharing systems, this paper investigates the effects of transmit diversity on the peak interference power limited cognitive radio(CR) networks. In particular, we derive the ergodic and outage capacities of a spectrum-sharing system with multiple transmit-antennas. To derive the capacities, peak interference power constraint is imposed to protect the primary receiver. In a CR transmitter and receiver pair with multiple antennas at the transmitter side, the allowable transmit power is distributed over the transmit-antennas to achieve transmit diversity at the receiver. We investigate the effect of this power distribution when a peak interference power constraint is imposed to protect the primary receiver. We show that the transmit diversity does not improve the ergodic capacity compared to the single-antenna system. On the other hand, the transmit diversity significantly improves the outage capacity. For example, two transmit-antennas improve the outage capacity 10 times compared to the single-antenna with a 0 dB interference constraint.