The phrase 'accepted by many' is correct and can be used in written English.
For example, "The scientific theory was accepted by many in the research field."
But it's not accepted by many – the authorities included.
Among them, kinematic analysis, an unsupervised and data-based method, has been accepted by many researchers.
The base standard that covers medical devices, IEC 60601-1, is accepted by many countries.
It was not accepted by many of the Hutu majority in Rwanda.
Private insurance pays more and is accepted by many more doctors.
It is so widespread that defensive medicine is accepted by many physicians as normal.
Living with one that still is not accepted by many is so much harder.
The principle of trading of agriculture against Nama had been reluctantly accepted by many at the WTO.
In the mood of resentment created by the treaty, the claim was readily accepted by many Germans.
The West Midlands already has boundaries accepted by many organisations and a rapidly strengthening regional local-government organisation.
The sequestration cuts, now accepted by many Republicans, as the White House notes, provide no permanent entitlement changes.
