Have we underestimated Yoko Ono all along? (And did she keep the Beatles together?)

In September 1966, John Lennon, who had just finished what would be the Beatles’ last world tour, visited an exhibition, “Unfinished Paintings and Objects.” Featuring the work of Japanese-born American artist Yoko Ono, it was scheduled to open in London the next day.

Spying a stand with a note saying “Apple,” Lennon took a bite. When he realized he had wrecked Ono’s sculpture and hoping to atone, Lennon asked if he could participate in “Painting to Hammer a Nail (No.9).”

“It’s so symbolic, you see — the virginal board,” Yoko explained, before agreeing to let him bang it for five shillings. “Well, I’ll give you an imaginary five shillings and hammer an imaginary nail in,” Lennon replied. “And that’s when we really met,” he subsequently said. “That’s when we locked eyes and she got it and I got it.”

In “Yoko,” David Sheff — author, among other books, of “Beautiful Boy,” which borrows its title from a Lennon song and is about Sheff’s son’s struggle with addiction — examines the life and work of a multifaceted woman. Her name is recognized around the world, but little is known about her life, outside of her connection to Lennon.

Sheff interviewed the couple for an article in Playboy in 1980, shortly before Lennon was murdered, and remained friends with Ono. Taking full advantage of his access to her, his biography manages to be celebratory without losing sight of her idiosyncrasies, flaws and failures.

Sheff quotes extensively from scathing reviews of Ono’s singing and her avant-garde art installations. He explains how her reliance on tarot cards, psychics and astrologers, along with bouts of loneliness, depression and fear, made her ripe for exploitation.

That said, he also makes a compelling class that claims that she was responsible for breaking up the Beatles are a “tired myth.” With the Fab Four already at odds with one another and tired of the demands of superstardom, Sheff writes, if Ono had not accompanied Lennon to recording sessions and the set of “Let It Be,” he “might not have shown up at all.”

Ono not only inspired “Imagine,” the most acclaimed song of Lennon’s solo career, but she co-wrote the lyrics with him. Ironically and inaccurately, “Imagine” was sometimes credited to Lennon and Paul McCartney (initially not credited for the song, Ono was finally recognized for her contributions in 2017).

And when Lennon told a reporter that the purpose of the couple’s anti-Vietnam war “bed-in” was to insist, “All we are saying is give peace a chance,” it was Ono who suggested that the sentence should be converted into a song. The classic was recorded in a hotel room in Montreal on the last day of the bed-in, with a gaggle of celebrities — Timothy Leary, Tommy Smothers, Allen Ginsberg, and Dick Gregory — chanting the chorus.

Throughout her life, Yoko Ono has been a target of misogyny and racism. Until recently, Sheff maintains, her identity as Mrs. John Lennon and her roles as celebrity widow and radical political activist contributed to an underestimation of her talent as an artist.

As more of her albums have been released and the number of art exhibitions has mounted, however, Ono has increasingly been recognized for what one critic called “the breadth, charm and brilliance of her output.”

After Lennon was murdered, Ono often said her only goal was survival. She has accomplished far more than that, Sheff concludes, creating work “that edified, enlightened and inspired,” while challenging millions of people to imagine ”a better world.”

Glenn C. Altschuler is an emeritus professor of American Studies at Cornell University.

Yoko: A Biography

By: David Sheff.

Publisher: Simon & Schuster, 346 pages, $30.