We can factor $g$ into a product of irreducible elements.

Note that the apparently [= seemingly] infinite product in the denominator is in fact finite.

Then $P$ is the product of several integer factors of about $x^n$ in size.

We need to check that $F$-derivatives behave in the way we expect with regard to sums, scalar multiples and products.

A different notation is used because the usual tensor product symbol is reserved for the tensor product of $A$-bimodules.

Then $B(E)$ is a unital Banach algebra with product the composition of operators.

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