Can art take love's place?; Look at Me, by Anita Brookner. New York: Pantheon Books. 192 pp. $11.95.

Art alone does not make a life. It can provide some solace for the ego, some relief for the heart, but it cannot substitute for a happy life well lived. Frances Hinton, the narrator of ''Look at Me,'' is a single woman, still of marriageable age, who works as a librarian in a medical research library. Like many people, Frances desires a life other than the one she has. She has a talent for writing, but this she views as very much a last resort.

At the library she meets Nick, a handsome young doctor, and his glamorous wife, Alix. They represent to Frances everything she is not and would like to be. Through Nick and Alix, Frances meets a man, shy and unglamorous like herself , who seems to promise, at last, an opportunity for love. But it does not work out, and Frances chooses to live alone with her talent for writing.

Though ''Look at Me'' never falls to the level of the merely dolorous, it is not a book that pulls punches. Those looking for a lighthearted romance would be advised to choose something else.

Anita Brookner is not a full-time author but a highly respected art historian at London's Courtald Institute of Art, who writes during vacations. She has said that her own attitude toward writing is similar to her narrator's in ''Look at Me'':

''It was then that I saw the business of writing for what it truly was and is to me. It is your penance for not being lucky. It is an attempt to reach others and make them love you. . . ''

It will be interesting to see if Anita Brookner, in novels to come, will address the question of why those who have been blessed with full lives and an adequate outlet for love often regard those with artistic talent as existing on a more exalted, if sometimes lonelier, plane.