| Let Aphi be a truncated Toeplitz operator -- the compression of the Hardy space Toeplitz operator T phi to the model space H2 ⊖ uH2, where u is a nonconstant inner function. We find a necessary and sufficient condition that the product AF1AF2 is itself a truncated Toeplitz operator. Specifically, we show that there are algebras of truncated Toeplitz operators Ba (depending on alpha ∈ C* ) such that two truncated Toeplitz operators have a truncated Toeplitz operator as a product if they are both in the same Ba . Some consequences of this are also discussed. |
