Hours after Soviet leader Mikhail Gorbachev returned here from the Geneva summit last Friday, the state-controlled television began playing George Gershwin and Glenn Miller and put a small crack in the wall built up by six years of brittle U.S.-Soviet relations.

In the week since Gorbachev and President Reagan established warm personal contact at Geneva, while failing to make any visible progress on arms control and other political problems, American names and faces that had been absent from the Soviet media for several years have started popping up again.

Business contacts for Americans dealing with the Soviet Union reportedly loosened overnight following statements from Gorbachev in Geneva and on his return here that the Soviet Union is "ready to invite U.S. business circles to take part in carrying out large projects" now that he and Reagan have, to some extent, cleared the air.

Initial Soviet reactions to the signing of a new U.S.-Soviet cultural exchange program and to Gorbachev's new emphasis on what he called "this sphere of mutual economic relations" at Geneva suggest that Moscow views the summit as having opened the way for a return to some form of economic and cultural detente even if superpower political relations remain difficult.

"The mood has been so bad between the two countries, it has to get better," a Soviet official said. "It all has to start with little steps."

In a postsummit speech on Nov. 21, Gorbachev sent out a call for improved U.S.-Soviet relations, and the government media and individual Muscovites alike have wasted no time in responding.

Shortly after Gorbachev's return from the summit last Friday, national television broadcast some songs by American and other foreign composers, including Gershwin and Alan J. Lerner and Frederick Lowe. American music on state-controlled radio and television is rare in the Soviet Union. The next day, the front page of the Communist Party newspaper Pravda carried a poem -- entitled "Geneva" -- that expressed trust and hope that the summit spirit would continue.

At a press conference concluding the summit, Gorbachev said he had told Reagan "one must never underestimate this sphere of economic mutual relations. . . . This is the material base for political relations, a base for the improvement of relations. . . . Openly speaking, through the economy we get more dependent on each other, and this dependence is then also reflected in the solution of political problems."

The response has been rapid.

Avon called on Moscow, according to the Soviet news agency Tass, and signed a contract Tuesday to supply and develop cosmetics, hold seminars, and open new ventures here. IBM executives came, too, Soviet sources report, and conducted talks about supplying the Soviet Union with computers. Next week, a delegation of about 300 American businessmen -- the largest from the United States since 1982 -- is expected here for a U.S.-Soviet Trade Council meeting.

Plans for the meeting were made before the Reagan-Gorbachev summit, but American businessmen here expect the improved tone in U.S.-Soviet relations to lift the atmosphere during their discussions here.

But no matter how insignificant they seem to westerners, Muscovites already have been impressed with a few tangible signs of a fresh wind in U.S.-Soviet relations.

A few days ago, Soviet television viewers watched "Love Among the Ruins," starring Katharine Hepburn and Laurence Olivier, the first American film Soviet viewers recall seeing on television in months.

A boys choir from San Francisco, touring the Soviet Union, also appeared on television, and drew loud applause in Moscow living rooms.

The Soviet Union plans to publish a book about longevity in Soviet Georgia by American author Paula Garp, according to the Moscow newspaper Sovyetskaya Rossiya.

"It seems," said one Moscow housewife, "that an attempt is being made to open up a little toward the United States."

Soviets, too, expect to reap benefits from the revived exchange program. In two weeks, the Soviet national soccer team will make a tour of the United States.