Hilbert space unconditional bases formed by values of an entire vector-function of order 1/2

Let $B$ a dissipative Volterra operator in a separable Hilbert space $\mathfrak H$ such that the resolvent $(I-zB)^{-1}$ has finite exponential type. A complete description is given of the operators $B$ with the above properties, vectors $g\in\mathfrak H$, and sequences $\Lambda$ of complex numbers such that the family
$$ (I-\lambda_kB^2)^{-1}, \quad \lambda_k\in\Lambda, $$
forms an unconditional basis in $\mathfrak H$.