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Los Angeles (CNN) — Famed actress Elizabeth Taylor has shown “steady improvement” since she was taken to a Los Angeles hospital last week for treatment of a heart problem, her representative said.

Taylor, 78, has been “comfortable over the past few days,” according to a statement released Tuesday afternoon.

She checked into Cedars-Sinai Medical Center a week ago for “symptoms caused by congestive heart failure,” which an “ongoing condition,” representative Jamie Caldwell said last week.

“Since being admitted, there has been steady improvement in her condition,” the latest statement said.

Taylor will stay at Cedars-Sinai for “continued monitoring,” the statement said.

“Her medical team is gratified by her progress to date, and it is hoped and expected that this will continue over the next few days,” it said.

The London-born movie star has won two Academy Awards for best actress: for “Butterfield 8” in 1961 and “Who’s Afraid of Virginia Woolf” in 1967.

When doctors repaired a leaky heart valve in October 2009, Taylor posted a Twitter message saying it “was like having a brand new ticker.”

The actress has used Twitter over the past two years to communicate with fans and dispel the occasional rumor reported on celebrity gossip websites.

However, a message she tweeted last Wednesday was her first in nearly six months. The tweet pointed fans to an interview she gave to Kim Kardashian in Harper’s Bazaar magazine.

“I like the connection with fans and people who have been supportive of me.” Taylor told Kardashian when asked about Twitter. “And I love the idea of real feedback and a two-way street, which is very, very modern. But sometimes I think we know too much about our idols and that spoils the dream. So, like all things, it is to be used with care!”