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We analyze strict dissipativity of generalized linear quadratic optimalcontrol problems on Hilbert spaces. Here, the term ``generalized'' refers tocost functions containing both quadratic and linear terms. We characterizestrict pre-dissipativity with a quadratic storage function via coercivity of aparticular Lyapunov-like quadratic form. Further, we show that under anadditional algebraic assumption, strict pre-dissipativity can be strengthenedto strict dissipativity. Last, we relate the obtained characterizations ofdissipativity with exponential detectability.

Strict dissipativity for generalized linear-quadratic problems in infinite dimensions