Japan is warily welcoming Donald Trump as the US president, wondering what his administration will mean for their security alliance and already seeing what it means for their trade relationship.

But there are no such mixed feelings about Mr Trump's eldest daughter: Ivanka Trump is widely revered as the perfect woman here.

Among some Japanese women, Ms Trump is seen as an aspirational figure who has combined motherhood and career while managing to look perfectly put-together all the time (although her glamorous Instagram photos never show the retinues of nannies and assistants and hairdressers that answer the question of “how does she do it all?”).

The Obamas and Ivanka Trump will be neighbours in DC's Kolorama

Japan remains a highly patriarchal society, where men spend long hours at the office and women are often expected to give up their jobs after getting married or having babies.

But Ms Trump offers an example of how to be strong but not scary, said Yuriko Shinzato, 32, a freelance writer and mother of a 6-year-old daughter. “She is a good example that a woman can do an outstanding job and handle a misogynist father like Trump, without pushing too much of a feminist agenda or confronting men too much,” Ms Shinzato, who blogs about Ivanka Trump's fashion and lifestyle, told the Japan Times. “That is something that Japanese women want but have a hard time doing in a still male-dominated society.”

As a result, the Trump daughter has quite a following here. The Japanese internet was abuzz after the election at a tabloid report that Trump might be the next American ambassador to Japan, and she won Japanese fans when she posted a video of her daughter, Arabella Rose, performing the song “Pen-Pineapple-Apple-Pen” by the Japanese comedian known as Piko Taro.

Japanese women gush about her on social media. “This is the woman I like now. Ivanka Trump. I love it that she’s not only beautiful but also clever and has a graceful air. I think women should be kind and gentle,” wrote Sachiko W on a portrait that Ms Trump had posted on Instagram.

On Twitter, news announcer Mari Maeda posted a photo of Trump in the lobby of Trump Tower in New York. “Trump’s eldest daughter Ivanka-san, who made it into the administration transfer team. She waved at me when I called out to her at the Trump Tower,” Ms Maeda wrote. “What a figure she has even after having three children. So frank and cute! Her jewelry brand is popular but some fans say they want her to become the president because of her intelligence and beauty.”

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This popularity is translating into increased demand for Ms Trump’s fashion business in Japan. Sales have skyrocketed since Mr Trump's victory in the US presidential election — although from a very low, almost negligible, base.

“Ivanka Trump, a woman gifted with both intelligence and beauty, is gathering attention as a daughter of the next US president Donald Trump. She introduces dresses, jewelry and bags under her own brand,” Waja, a popular Japanese online retailer, says on its Ivanka Trump page, which sells handbags and dresses. “Her brand, though in a reasonable price range, is well-reputed for its high quality and enjoys tremendous popularity among working women thanks to its feminine and elegant designs and silhouette.”

The Ivanka Trump page on Waja used to average some 30 hits a day before the 8 November election. By 14 November, it was racking up 10,000 hits a day, although that has since tapered off to about 500 hits a day. Sales are booming in relative terms. Before the election, Waja sold only a few Ivanka Trump dresses a month, said spokeswoman Yukie Suzuki. But it sold 170 dresses in November — 28 times as many as the year before — and another 140 frocks in December.

Ms Suzuki thinks sales will continue apace because the brand perfectly matches Waja’s target demographic — working women in their 40s who are looking for something they can wear to work and then out afterward. It’s “sophisticated, elegant and feminine” yet “reasonably priced,” Ms Suzuki said.

The Ivanka Trump site on Buyma, the Japanese equivalent of eBay’s fashion pages, has also been enjoying a post-election boost, although from a very low base, a spokesman said.

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In the United States, Ivanka Trump’s sales suffered during the presidential campaign amid revelations of statements that her father had made about women. Ms Trump found herself in hot water in November after it emerged that she had been in talks with a Japanese company, partly owned by a Japanese government agency, when she attended a meeting between her father and Japanese Prime Minister Shinzo Abe the week after the election.

The New York Times reported that Ms Trump's clothing company had been in talks about a licensing deal with Sanei International, a clothing company owned by TSI Holdings. TSI’s biggest shareholder is the Development Bank of Japan, a financial institution owned by the Japanese government.

Kohei Yamada, a spokesman for TSI Holdings, said on Tuesday that the negotiations were still ongoing and that nothing had changed since the meeting between the Trumps and mr Abe.

Since her father’s election and her husband’s appointment as a White House adviser, Trump has stepped away from her name-brand fashion, jewelry and licensing companies.