PARIS, France — LVMH is making a $2.6 billion bet that the same consumers who can spend $1,000 on a Louis Vuitton bag will splash out for a $2,000-a-night hotel on Italy's Amalfi Coast.The French luxury giant agreed to buy Belmond Ltd., owner of New York's '21' Club and high-end resorts around the world. The transaction is LVMH's largest since taking full control of Christian Dior for more than $7 billion last year and pushes the company further into services amid rising concern about the sustainability of the Chinese demand that's driven fashion industry growth.LVMH agreed to pay $25 a share in cash for London-based Belmond, a 42 percent premium over its closing price in the US on Thursday. The Paris-based company's shares fell as much as 3.1 percent early Friday.The acquisition is one of LVMH founder Bernard Arnault's biggest, rivaling the purchases of Bulgari and Loro Piana. It comes as consumers shift spending toward trips, health clubs, restaurants and entertainment and interest in shopping malls dwindles.The company’s shares are down 18 percent since September on concern that Chinese buyers who account for about a third of industry sales and a majority of growth don’t have room in their closets for more leather goods and fashions. Luxury-industry revenue is likely to grow 5 percent in 2019, slowing from a rate of more than 10 percent this year, according to analysts at Goldman Sachs.The acquisition addresses another challenge facing LVMH and rivals Kering SA and Richemont. They've snapped up so many of the world's leading brands that there are few prominent leather and couture labels left to buy. The Louis Vuitton owner, formed through a merger with Champagne and cognac maker Moet Hennessy, has already expanded into perfume, watches, jewelry and cosmetics retail. Prominent remaining independents like Chanel and Hermès have shown little inclination to sell.The deal will expand the French company's high-end hospitality offerings. LVMH formed a hotel management group in 2010 to oversee its operations in the sector, which include properties under the Cheval Blanc name in locations like the Courchevel ski resort in the French Alps. LVMH's Bulgari jewellery brand has six hotels, including one in Shanghai that opened in July. It plans to open hotels in Moscow, Paris and Tokyo in the next four years.Aside from the deal for the rest of Christian Dior, which LVMH already controlled, the French conglomerate had been relatively quiet on the mergers-and-acquisitions front since buying German suitcase maker Rimowa in 2016.‘21’ ClubBelmond, which used to be known as Orient-Express Hotels, owns or has stakes in more than 30 high-end hotels around the world, from St. Petersburg to Anguilla in the Caribbean. In addition to the ‘21’ Club power restaurant in Manhattan, its stable of luxury properties includes a cruise line in France, a London-to-Venice train line and safari camps in Botswana.The agreement ends a four-month sale process as the company has sought to take advantage of a strong hospitality market. The company said in August it hired Goldman Sachs Group Inc. and JPMorgan Chase & Co. for a strategic review. Analysts speculated a sale could involve breaking up the company's assets, since its properties could be of value as trophies for ultra-wealthy investors including sultans and oligarchs.The company’s shares have soared 58 percent since August 8, at one point reaching their highest level since 2008. They closed at $17.65 in New York trading on Thursday.LVMH is a surprise winner for Belmond. Among those weighing an offer for all or part of the company were KSL Capital Partners LLC, Blackstone Group LP, KKR & Co. and Ashkenazy Acquisition Corp., people familiar with the matter told Bloomberg in October.By Robert Williams, Jeff Sutherland; Editors: Eric Pfanner, K. Oanh Ha, Thomas Mulier.