Holomorphic subordinated semigroups

If (e−tA)t>0 is a strongly continuous and contractive semigroup on a complex Banach space B, then −(−A)�, 0 < � < 1, generates a holomorphic semigroup on B. This was proved by K. Yosida in (7). Using similar techniques, we present a class H of Bernstein functions such that for all f ∈ H, the operator −f(−A) generates a holomorphic semigroup.