This paper studies dissipativity for a class of infinite-dimensional systems, called pseudorational, in the behavioral context. Extending the finite-dimensional counterpart, we show that a pseudorational behavior is dissipative if and only if it admits a storage function or a dissipation function. For its proof, we derive a new necessary and sufficient condition for entire functions of exponential type in the so called Paley-Wiener class to allow a symmetric factorization. Characterization of dissipative behaviors and linear quadratic optimal behaviors are also given.