I am wondering whether the following sentence is punctuated properly:

From the previous section, the operator A is skew-adjoint; has compact resolvents; and thus has the required conditions.

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No. All the semicolons should be commas. See this wonderfully handy resource, The Punctuation Guide.

Semicolons go

  • Between independent clauses when a coordinating conjunction is omitted
  • Between independent clauses linked by a transitional expression
  • In lists with internal commas
  • In elliptical constructions

This sentence doesn't contain any of these constructions.

It would still be an awkward sentence, though. It might be clearer like this:

"From the previous section, the operator A has the required conditions because it is skew-adjoint and has compact resolvents."

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