Michael Kovac/FilmMagic
February 15, 2011 05:30 PM

It’s good news for Elizabeth Taylor!

A week after checking into an L.A. hospital for symptoms associated with congestive heart failure, the Hollywood icon is showing marked improvement, PEOPLE has learned.

“Since being admitted, there has been steady improvement in her condition, and over the weekend she has had visits from family and close friends,” says a statement from reps for the legendary actress, 78, who suffers from an ongoing heart condition. “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. For now, she will remain under their care in the hospital for continued monitoring.”

While Taylor is enjoying visits from those close to her, “she is sleeping and resting a lot, which she really needs to recover her strength,” the star’s rep Sally Morrison tells PEOPLE. “Due to symptoms of congestive heart failure, she is still being monitored and continues to need rest to recover her strength. She did not have a heart attack.”

Symptoms of congestive heart failure include difficulty breathing and fluid in the lungs.

Taylor, who underwent heart surgery in October 2009, appreciates support of her loyal fans. As the statement continues: “Friends and fans around the world should be reassured that Elizabeth Taylor is in good hands and receiving the best possible care from her skilled and dedicated doctors and nurses.”

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