February 20, 1983

Claudio Arrau's piano recital at Avery Fisher Hall this afternoon will celebrate his 80th birthday and, at the same time, bestow a twofold gift on his listeners. For every so often, nature produces a musician who achieves great age without relinquishing his powers of communication, and events like today's not only compress 70-odd years of practical performing experience into two hours of music; they tell us in fascinating ways how age can transform how we think and how we hear. Few of the living can see Mr. Arrau's career as a whole - it stretches far too far into the past. But clearly this long musical life - begun in Chile in 1903 and nurtured in Berlin before World War I- serves as connective tissue between the emotional generosity of the Romantic era and the respectful restraint of mid-20th century interpretive philosophy. Mr. Arrau's teacher in those Berlin years was Martin Krause - a pupil of Liszt. Yet it has been in the 1950's, 60's and 70's - an age of new classicism among performers - that Mr. Arrau's major recording projects have taken place. Rarely have two separate traditions been so successfully bonded together in one man, and for those who cannot share today's concert, there is the phonograph to assure us that all these qualities are really there.

ticket brochure proclaims, ''Billy's back!'' Bumper stickers shout, ''Billy's back!'' Billboards blare, ''Billy's back!'' And everyone asks, ''For how long?'' The contract that Billy Martin signed Jan. 11 says for five years; the skeptics say contracts between Billy Martin and George Steinbrenner have not been completed twice before. Billy and George. They are perhaps a more widely discussed couple than Elizabeth Taylor and Richard Burton ever were. They have forged a link that makes them as familiar a pairing as Abbott and Costello or Roy Rogers and Trigger. They are so well known they transcend the sports pages. They have wound up, for example, on the comic pages.

WITH divorce so common and New York City apartments so hard to find, the question of who keeps thea partment when a couple breaks up has taken on new importance. An additional element is added to the situation when there is a p rospect of a conversion to a cooperative. Whoever gets the a partment may be able to buy it at a bargain insider price in a c onversion. There are many other questions involving real estate thatp arting couples may quarrel over, usually when property is owned. Butr ental situations offer special complications. Lawyers offer conflicting advice, but many agree that when it comes to maintaining the right to stay in possession of an apartment, there is a ''best'' position to be in, which can be determined by a few key questions: - Did you occupy the apartment before the marriage? - Is your name on the lease?

ATLANTIC CITY SINCE the opening of its first hotel-casino in 1978, this resort often has been called Las Vegas East. But if the swift growth here continues, Las Vegas may become Atlantic City West. Last year, with nine casinos its prime attraction, Atlantic City had 23.1 million visitors, double the 11.6 million for Las Vegas. The Atlantic City totals (up 21 percent from 1981) were announced last week by the city's Convention and Visitors Bureau and the New Jersey Expressway Authority.

Moshe Arens, who is replacing Ariel Sharon as Israel's Defense Minister, says that Israeli-American relations have worsened in recent months partly because of the Reagan Administration's attitude toward talks on Lebanon. Mr. Arens says the problem, in his view, is that some American officials have ''idealized notions'' about how quickly a negotiated solution can be achieved in Lebanon. In his first interview since being named to the Cabinet on Monday, Mr. Arens said the United States had benefited from Israeli military gains in Lebanon last summer. But, he added, ''You have got some people in the Administration who would like to pick up the dividends and kick us in the teeth at the same time.''