The phrase "a number of established" is correct and usable in written English.
It can be used when referring to several recognized or well-known entities, practices, or concepts in a particular context.
Example: "A number of established theories in physics have been challenged by recent discoveries."
Alternatives: "several recognized" or "various well-known".
A number of established CBS shows are staying in their time slots next season.
Camping is available in a number of established campsites, as well as in primitive sites along the Siltcoos river.
Bailey is one of a number of established stars snapped up by Sky1's new controller, Stuart Murphy, to front shows for the channel's autumn and winter lineup.
American inventor of what was probably the first commercially successful electric motor, which he used with great ingenuity to power a number of established inventions.
Since reunification, it has attracted a number of established and aspiring writers — all drawn to its openness and support for artistic expression.
Tim Cahill of the Red Bulls has played for a number of established coaches, including David Moyes at Everton and Guus Hiddink with Australia's national team.
There was Frank Sinatra's ex-wife Nancy, as well as a number of established couples — the Jack Bennys, the Joel McCreas, the William Holdens.
Many know by now that the orchestra, an international assemblage that includes a number of established soloists and chamber musicians, gathers at the Swiss festival every summer out of respect and affection for Mr. Abbado.
It was not just that experiences with similar institutions elsewhere were ignored – and academic discussion of them not taken into account – but that a number of established principles for such bodies were actually violated.
Bloomberg reports that Chandler has spent up to four million dollars renovating a fourteen-thousand-square-foot space at 24 West 57th Street, the building that's already home to a number of established dealers including Marian Goodman.
And a number of established businesses are setting up Internet operations with a view to spinning them off: Freeserve, Britain's first free ISP, was set up by Dixons, a retailer.But this is not enough.
