An empty sea of asphalt surrounds the Eastern Airlines Reservation Center in Salt Lake City just purchased by Peter V. Ueberroth and a group of investors for $464 million.

Inside, computer-printed banners hang above the doors: "Keep our dream flying."News of the airline's new owner was cheered by Salt Lake employees, who have been idled for a month by the strike that brought Frank Lorenzo's airline to its knees. Local Eastern employees, representing various sides of the labor dispute, echoed their national colleagues: Each group agreed they were cautiously optimistic about the prospect of being back to work soon.

Terms of the sale were announced Thursday. But Eastern's major creditors, federal bankruptcy court and three unions - including the International Association of Machinists that initiated the strike March 4 - still have to approve on the deal.

The major concern for Salt Lake employees is whether the airline will continue flying national routes, or concentrate on rebuilding its East Coast routes.

Bob Burquist, who directs the Salt Lake reservation center, said he expects Salt Lake City to be among the first two or three reservation centers that reopens once negotiations end. He said Salt Lake's elaborate WATS network integrates well with the national system and can function even if the initial focus is on the East Coast.

"I think we are cautiously optimistic and we are ready to go back to work," Burquist said. "I think we've heard from all 650 clerks in the past 24 hours, and most said they could be back to work with an hour's notice."

"You have to realize that while the rank and file are excited, you're still dealing with the same union leaders and you're talking about the same kinds of concessions," Burquist cautioned. "The pilots, flight attendants and the non-contract employees have each taken a 20 percent cutback in recent years, and they'll be looking closely at what the machinists do - whether they're willing to belly up also."

Airport Director Lou Miller said he is confident the airline's new owner will need a reservation facility in the West. "I suspect they'll open it up again," he said.

Also about 50 members of AFL-CIO affiliated unions picketed Continental Airlines on Thursday, another Lorenzo-owned airline, at the Salt Lake International Airport to show support for Eastern's unions.

"Even though the sale was in the works, we were instructed to go ahead with our plans, even here in Salt Lake City," AFL-CIO President Eddie Mayne said.

Veteran reservation clerk Judy Murphy said most of the 650 non-union agents laid off are just waiting for a telephone call from their former bosses. "I think it's a good sign. I think most people would go back if they called them back. Very few that I've heard of have gone on to other things," she said.

Roger Murray, Eastern sales manager and one of only four employees at the Salt Lake Reservation Center who continued drawing paychecks during the strike, told former agents who telephoned Thursday afternoon that he hoped to see them soon.

"There is so much to this. I don't know if we're going to be back to 3,000 employees (strong) Monday, because we've lost so much of our passenger base, " Murray said.

Murphy praised Ueberroth, who said Thursday that his reorganization plans include both the unions and Eastern's non-contract employees. "That's positive for us, because we're usually left out. If you notice, whenever they have meetings they talk about the three unions and they don't mention us."

Pilot Bruce Quigley said his colleagues are ready to don Eastern wings and fly for Ueberroth. "It's all very conditional. We're very, very skeptical, very cautious. I'm very cynical. I love my fellow man, but with Eastern Airlines, I'm cynical as all get out."

Quigley said members of the machinists union know the pilots want to fly for Ueberroth. He said 80 percent of Eastern's pilots planned to cross picket lines, until Lorenzo asked for additional 11th-hour concessions. The union also agreed to a 20 percent pay cut in 1986, as the non-contract employees did, in order to save the faltering airline.

"First of all, this is their strike. They haven't given any. They have to give up their share."