L Brands Inc. is near a deal to sell control of Victoria’s Secret to a private-equity firm in a transaction that values the lingerie brand at about $1.1 billion, according to people familiar with the matter.

Sycamore Partners is expected to buy 55% of Victoria’s Secret and take the struggling business private, the people said. L Brands is expected to keep a 45% stake in the separate company, which will include the Pink chain. After shedding several brands in recent years, L Brands’ operations would be reduced to running the…

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