July 20 marks the 45th anniversary of the death of Bruce Lee, who had one of the briefest and most remarkable careers in Hollywood history. On July 23, 1973, Variety ran his 300-word obituary on page 7. He didn’t get star treatment because he wasn’t yet a star, at least in the English-speaking world. As Matthew Polly points out in his excellent new bio “Bruce Lee: A Life” (Simon & Schuster), Lee had a career in Asia as a child actor, a dancer (he won Hong Kong’s 1958 Cha-Cha Dance Championship with little brother Robert), a young star (nicknamed “Little Dragon” by his fans) and then a martial-arts practitioner and innovator. The rest of the world discovered him when “Enter the Dragon” opened in 1973, just one month after he died suddenly at age 32. (The cause of death was originally listed as acute cerebral edema, but Polly writes about various other theories for his death.) Variety reviewer Whitney Williams enthused, “Lee socks over a performance seldom equaled in action (movies).” His charisma, good looks and dazzling moves ensured him a posthumous legacy as a star, and as someone who laid the groundwork to bridge the styles of East and West.

He was born Lee Jung-fan in San Francisco, where his father was acting with the Cantonese Opera Company. The family returned to Asia, and Lee began appearing in films at age 6; in 1960, he starred in “The Orphan” as an angry teenager, evoking memories of “Rebel Without a Cause.” It was one of many times he was compared with actor James Dean.

Lee returned to the U.S. where he enrolled at the University of Washington and wrote a master’s thesis that was later expanded into 1963 paperback “Chinese Kung Fu: The Philosophical Art of Self-Defense.” He opened a martial arts school in Seattle, then moved to Los Angeles to pursue his Hollywood dreams.

Lee played sidekick Kato in the series “The Green Hornet,” which lasted 26 episodes starting in 1966. An item in the Aug. 7, 1968, weekly Variety pointed to a big-screen project: “Bruce Lee, an expert on Jeet Kune Do, the Chinese art of using feet as lethal weapons, will stage the fight sequences and also play a role in MGM’s ‘The Little Sister.’ ” (The Raymond Chandler adaptation was retitled “Marlowe.”)

At that point, Western awareness of martial arts was limited, and most of it was centered on judo and karate. As Polly explains in his book, Lee created Jeet Kune Do as “a means of self-defense and self-enlightenment.” It was a hybrid of East and West, of martial arts, philosophy and mysticism, incorporating movements from boxing, kung fu, fencing and other sources.

In Los Angeles, Lee picked up other jobs, including a recurring role in the 1971 series “Longstreet,” and he tutored stars like Steve McQueen and James Coburn in martial arts. But he grew frustrated at seeing Caucasian stars in “yellowface” get leading roles as Asians. (As Lee got closer to stardom, he was crushed to see David Carradine cast in the series “Kung Fu.”)

He returned to Hong Kong with wife Linda and their two children, and he and producer Raymond Chow formed Golden Harvest. He made several hit films and then returned to Hollywood. He finally achieved his goal of becoming the first Asian global superstar, but did so posthumously.

According to the wishes of the widowed Linda, Lee mixed East and West even in death; he was buried in Seattle with a gravestone that was hand-carved in Hong Kong, identifying him as “Founder of Jeet Kune Do.”

In Dec. 27, 1973, Variety did a front-page story and chart summarizing the year’s “top key-city grossers.” The story said the star system was thriving, with most top films sporting marquee names. Among the stars with two films in the year’s top 50 were Barbra Streisand, Robert Redford, Gene Hackman — and Lee. “Enter the Dragon” was No. 20 for the year, with “The Chinese Connection” at No. 47.

The following month, Variety ran an unbylined story about martial arts action films, which had ballooned in popularity after years of being limited to “ethnic houses in the Chinatowns of major American cities.” The story said it was unclear at that point whether martial arts films would be a fad or become a lasting film genre, “but karate and related elements will surely be incorporated into standard actioners in the future.”

The story said that one reason was Lee, who died suddenly “before he could capitalize on his fame. Bruce Lee posters are now available in most cities, giving the actor a James Dean aura in some quarters.”

Like Dean, Lee created a legacy that lasted far beyond his few films. Forty-five years after his death, he is still a reminder that there is a huge audience for films starring Asian leading men.