Toeplitz operators (also called localization operators) are a generalization
    of the well-known anti-Wick pseudodifferential operators studied by Berezin and
    Shubin. When a Toeplitz operator is positive semi-definite and has trace one we
    call it a density Toeplitz operator. Such operators represent physical states
    in quantum mechanics. In the present paper we study several aspects of Toeplitz
    operators when their symbols belong to some well-known functional spaces (e.g.
    the Feichtinger algebra) and discuss (tentatively) their separability
    properties with an emphasis on the Gaussian case.

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