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algebra analytic functions Banach space block decomposition map closed graph theorem coefficients column complex vector space Corollary Let deg^a deg^T deg^X denotes differential operator divisors of zero entries equation equicontinuous exists a unique f e f f e P(E f tn F-space finite formal power series function spaces Hadamard multiplication Hausdorff hence infinite matrices integer Kothe linear map linear operator linear subspace locally convex locally convex topology Math matrix multiplication multiplication operator Note operations with power operator that commutes polynomial power series multiplication Proof Prop Proposition Let Proposition Suppose REGULAR REPRESENTATIONS seminorms sequence spaces shift operator subalgebra subspace of f substitution operator sup f tions topology defined translation vector valued sequence weighted multiplication