THESE 15 STORIES -- Arturo Vivante's most recent collection -- are disarmingly easy to read. They are short. Their style is clear. Their social world is reassuringly harmless: all genteel poverty and artistic temperament. Their predominant tone is affectionate nostalgia.

Most of the stories are slices of an Italian family saga and are set in roughly chronological order. Father is a philosopher whom other philosophers will not notice; mother is a painter who keeps her canvases in a cupboard. He is impractical, imperious; she is loving and loyal. Elder brother is a classics scholar, younger brother a mathematician, sister a tubercular bohemian.

Finally there is middle brother, the central character -- sometimes an unnamed "I," sometimes called simply "the son," sometimes identified as "Giacomo." Giacomo has studied medicine but has given up its practice to become an artist, an obvious stand-in for the figure of the writer.

The stories run from little Giacomo's idealized portrait of his mother, through the family's flight to England in 1938 (Giacomo's father is Jewish), through Giacomo's internment in Canada as an enemy alien, and onward, with gaps and repetitions, through the deaths of his parents, ending with his purchase of a home of his own in Italy.

This would be fine stuff for fiction, and what is disturbing about most of these stories is that their material is not treated as fiction. It is left unshaped, its importance undeveloped, its significance not pursued. It is merely remembered and reported, amounting to neither more nor less than life faithfully observed.

It is hard to feel, in fact, that some of these pieces are stories at all. Most of them lack the shape, the tension, the nerve, of fiction. Their principal method is not scenic but synoptic: there is a quality of summary, is looking back from a safe distance, many years later. Often they are less like fiction than reminiscence, less like stories than anecdotes. Or like a series of meditations, whose subjects (or occasions) are stated, like headings, in their titles: "The Orchard," "The Chest," "The Room," "The Bell" and so on.

It is entirely plausible that these events should be happening, in this order, to this central character. But fiction needs to go beyond the what, the when and the who, to make us understand the final why: why this character was made to undergo this experience, why this story was told to us, why it matters.

We may ask, too, whether many of these pieces have the independence to be stories. They share not only characters, subjects and style, but even minor details. What is wrong with being told in two stories that the bailiff carried money in his socks is simply that in both stories the fact is presented as new, and in one of them it cannot be. The integrity of a story's imaginary world is fractured by such duplications, which are unfortunately numerous.

The troubles with most of these pieces are underscored by contrast with two among them that clearly are stories, and good ones: "The Bed" and "The Soft Core." In each of these, something important is at stake -- in the first, marital love; in the second, final love. In both stories, characters come sharply into conflict, in scenes that are not rhetorically summarized but staged directly before us. The characters are real, the problems are real, the stories are crafted to focus our attention upon their cruxes. And we care.

By contrast, consider, from among the less successful pieces, "The Room." In this very short tale, the central character decides to repaint the bedroom of his dead mother; it has become a shrine to him. He does repaint it, and imagines her delight if she could know it. The story then ends.

Or a more ambitious story, "At the Dinner Table." Here the central character worries that his octogenarian father will be an embarrassment when guests come to dinner. The old man does well, however, and Giacomo winds up ashamed of having been ashamed. The story closes with an exchange between him and his wife:

"'You see, your father didn't spoil the evening,' Jessie said to him later, when they were alone.

"'He saved it,' Giacomo said."

This is bad because it doesn't extract significance, doesn't let the story open out in any direction: it merely points the obvious moral that the reader has long since seen for himself.

One feels, finally, that most of these stories fail by adhering too closely to autobiography -- by reporting a life rather than reshaping it, by being more interested in its circumstances than its importance. One cannot know whether the stories' subject is the historical "Arturo Vivante" or an invented "Giacomo," but that does not matter. Fiction must improve upon autobiography, even upon the autobiography of the unicorn.