Bounded symbols of Toeplitz operators on Paley-Wiener spaces and a weak factorization theorem

Key Points

• Any bounded Toeplitz operator on the Banach Paley-Wiener space can be represented with a bounded symbol, extending previous results.
• The continuous case of the Toeplitz commutator theorem is established, building on D. Sarason's findings in the discrete case.
• The weak factorization theorem shows specific function representations within Paley-Wiener spaces, illuminating operator relationships.
• Results indicate significant implications for the structure of Banach spaces and their associated operator behaviors.