‎‎As is known to Americans Mark Twain is a great American writer.
Replace “be known to”with “be known by”, why is this an error？

Question

Answer

These two sentences are equivalent:
"Americans know something."   (active voice)
"Something is known by Americans." (passive voice).

These are the same and are both correct:
"As Americans know, ..."
"As is known by Americans,..."

However, if you say "as is known to Americans", this phrase will be interpreted as an adjective phrase that modifies "Mark Twain".  You don't want that.  You want the phrase to modify the entire clause "M.T. is a great writer", not just "Mark Twain":

"It is known to Americans THAT Mark Twain is a great writer."

Answer

It’s not wrong to say  ’as is known by Americans  . .’    and is not an error ;  in fact it's the usual way to say this.
Sometimes when we are referring to people we say  ’. . is known to . .’  and it means the same as  ’. . is known by . .’

Answer

I think 'As is known to Americans, Mark Twain is a great American writer.'  is absolutely fine.

Answer

The original is awkward and unclear and the suggestion is worse. Depending on what you mean you can say:

Many Americans think that Mark Twain is a great writer. (It’s common knowledge that he is American)

I think Mark Twain is a great writer as do many Americans.

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