In the days after the election, Mr. Spencer led a Washington alt-right conference in chants of “Hail Trump!” But he also invoked Evola’s idea of a prehistoric and pre-Christian spirituality — referring to the awakening of whites, whom he called the Children of the Sun.

Image Evola, who died in 1974, is best known as a leading light of Traditionalism.

Mr. Spencer said “it means a tremendous amount” that Mr. Bannon was aware of Evola and other Traditionalist thinkers.

“Even if he hasn’t fully imbibed them and been changed by them, he is at least open to them,” he said. “He at least recognizes that they are there. That is a stark difference to the American conservative movement that either was ignorant of them or attempted to suppress them.”

Mr. Bannon, who did not return a request for comment for this article, is an avid and wide-ranging reader. He has spoken enthusiastically about everything from Sun Tzu’s “The Art of War” to “The Fourth Turning” by William Strauss and Neil Howe, which sees history in cycles of cataclysmic and order-obliterating change. His awareness of and reference to Evola in itself only reflects that reading. But some on the alt-right consider Mr. Bannon a door through which Evola’s ideas of a hierarchical society run by a spiritually superior caste can enter in a period of crisis.

“Evolists view his ship as coming in,” said Prof. Richard Drake at the University of Montana, who wrote about Evola in his book “The Revolutionary Mystique and Terrorism in Contemporary Italy.”

For some of them, it has been a long time coming.

“It’s the first time that an adviser to the American president knows Evola, or maybe has a Traditionalist formation,” said Gianfranco De Turris, an Evola biographer and apologist based in Rome who runs the Evola Foundation out of his apartment.

“If Bannon has these ideas, we have to see how he influences the politics of Trump,” he said.

A March article titled “An Establishment Conservative’s Guide to the Alt-Right” in Breitbart, the website then run by Mr. Bannon, included Evola as one of the thinkers in whose writings the “origins of the alternative right” could be found.