The nuclear ban that worked; Kennedy, Khrushchev, and the Test Ban, by Glenn T. Seaborg with Benjamin S. Loeb. Berkeley and Los Angeles: University of California Press. 320 pp. $16. 95.

This is one of the most important books to come from a university press within the past year. At a time of increased East-West tensions and stalled arms-control negotiations, it is salutary to be reminded that an effective weapons control treaty - the Limited (Nuclear Weapons) Test Ban Treaty - was successfully concluded between the United States and the Soviet Union and has been successfully maintained for nearly two decades.

Glenn Seaborg, Nobel Prize laureate, was chairman of the old Atomic Energy Commission (AEC) when the treaty was negotiated. With a decent time interval now past, he has opened the detailed diary he kept during his AEC tenure. Together with auxiliary materials, including interviews with other participants, he now has written an incisive account of events leading up to the treaty and of the negotiations and their successful conclusion.

It is, of course, a highly personal book - history as seen from the Seaborg perspective. Yet, as judged from another personal viewpoint, that of a reporter who covered some aspects of the test-ban story, Dr. Seaborg's account seems to be neither distorted nor unfair.

The test ban was the culmination of a great debate. Weapons testing in air and sea was increasingly polluting the environment. Although test proponents argued that the radioactive fallout was less dangerous than ''natural background radiation,'' this sounded disingenuous to an increasingly skeptical world. Test opponents argued that, at the very least, the nuclear powers had no right to subject the rest of humanity to the fallout.

It was a time when the US held a nuclear edge over the USSR. Thus test-ban proposals where hampered by mutual suspicions. The US suspected the Soviets wanted a test ban with minimal safeguards so they could ''cheat'' and catch up in nuclear capability. The Soviets suspected the US of wanting to freeze in its nuclear lead.

Many factors were at play during the late 1950s and early '60s, as the US, Britain, and the USSR repeatedly approached and backed off from a treaty that would at least ban those tests that could be monitored - in air, sea, and space - and for weapons above a certain power underground. However, it is Seaborg's thesis that the crucial factor was a personal relationship between President John F. Kennedy and Soviet Premier Nikita Khrushchev.

Sharp mutual antagonism gradually turned to mutual respect and a shared interest in arms control. Dr. Seaborg, of course, has no detailed information on Khrushchev's actions and attitudes, except as they were reflected in external effects. But he details many comments Kennedy made, many actions he took to win the test-ban agreement. His conviction that the relationship of these two men and their mutual search for effective arms control was a key factor in global politics is the main theme of his book. Indeed, he states that, had they lived, the world would likely have achieved even more effective arms control.

That's ''as may be,'' as the old Yankee saying goes. But Dr. Seaborg is surely right in warning that ''the hour (now) is late'' for seeking further arms control, for again stepping back from the dangers of the ongoing arms race. For giving an insider's view of what it takes to achieve such a step in East-West relations, Dr. Seaborg is to be thanked.