The Banach spaces and are not isomorphic

The statement of the title is proved. It follows from this that the spaces c 0 ( ℓ p ) , ℓ p ( c 0 ) and ℓ p ( ℓ q ) , 1 ⩽ p , q ⩽ + ∞ , make a family of mutually non-isomorphic Banach spaces.