The low housing inventory continues to push prices to up, as buyers scramble for luxury homes, Kofi Nartey of the Agency tells columnist Lauren Beale.

Zack Greinke has bought a gated home in Studio City for $4.575 million.

The Craftsman-style two-structure compound, built last year, features an art studio, bar, gym, library/study, media room, seven bedrooms, nine full bathrooms and two powder rooms. The more than 1 acre of grounds includes a nine-car motor court, swimming pool and a waterfall with a walking bridge.

Right-hander Greinke, 29, pitched a shutout against the Pittsburgh Pirates in his season opener for the Dodgers, but was later sidelined with a broken collarbone. The former American League Cy Young Award winner signed a six-year, $147-million contract with the ball club in December.

Rick Beck of Keller Williams in Beverly Hills was the listing agent, according to the Multiple Listing Service, and Bruce Dilbeck of Dilbeck Real Estate represented Greinke.

Meanwhile, Hyun-Jin Ryu, the Dodgers' new starting pitcher from South Korea, purchased a unit at the Ritz-Carlton Residences at L.A. Live.

The two-bedroom, three-bathroom condominium has 2,082 square feet of living space. Features include 10-foot-high ceilings, expansive windows and views of the Hollywood Hills, the ocean and the downtown skyline. The sales price was not disclosed, but similar units are listed at $1.8 million.

Building amenities include the tower's 26th-floor pool terrace, concierge service, a lounge with a wine-tasting room and glass billiard table, a media room and a fitness center.

The 26-year-old signed a six-year, $36-million deal with the Dodgers in December, after seven seasons with the Hanwha Eagles of Korea Professional Baseball. The rookie made his Major League Baseball debut in a series against the San Francisco Giants.

Mauricio Umansky and Billy Rose of the Agency in Beverly Hills were the listing agents.

A change of direction

Film director Joel Schumacher has put his longtime retreat in Carpinteria back on the market at $7.25 million.

Set on 5.5 acres, the compound includes a three-bedroom main house, a guesthouse and a two-bedroom caretaker's house. Built in 2000, the structures have a rustic feel and feature reclaimed barn wood. The main house includes a Diego Rivera-inspired mural entry. There are 5.5 bathrooms and 6,500 square feet of living space.

Schumacher, 73, gained recognition for his work on "St. Elmo's Fire" (1985), "Batman Forever" (1995) and "The Phantom of the Opera" (2004). He directed two recent episodes of the dramatic series "House of Cards."

Myra Nourmand of Nourmand & Associates in Beverly Hills and Riskin Associates of Village Properties in Montecito are the listing agents.