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We provide a general scheme to extend Taylor's holomorphic functional calculus for several commuting operators to classes of non-holomorphic functions. These classes of functions will depend on the growth of the operator valued forms that define the resolvent cohomology class. The proofs are based on a generalization of the so-called resolvent identity to several commuting operators.

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Abstract. We compute the essential Taylor spectrum of a tuple of analytic Toeplitz, where D is a strictly pseudoconvex domain. We also provide specific formulas for the index of T g provided that g −1 (0) is a compact subset of D.