sufficed condition for continuity of a operator between tempered distribution

Question

I know that if $f\in S'(\mathbb{R}^n)$, then $f$ is continuous iff $f$ is sequentially continuous

(you can see the result in https://books.google.com.br/books?id=XNSBDwAAQBAJ&pg=PA118&lpg=PA118&dq=sequentially+continuous+tempered+distribution&source=bl&ots=2urkrzJ97y&sig=ACfU3U0dyNvhoU6ViFhsecIpnKn4o4rxjQ&hl=pt-BR&sa=X&ved=2ahUKEwium5SEwfjpAhVLGbkGHfQAB0AQ6AEwA3oECAkQAQ#v=onepage&q=sequentially%20continuous%20tempered%20distribution&f=false)

What about a linear operator $T:S'(\mathbb{R}^n) \to S'(\mathbb{R}^n)$. If $T$ is sequentially continuous, does it imply that $T$ is continuous ?