Factorization and coincidence theorems for generalized adjoints.

As a consequence of a factorization theorem, we establish conditions on the Banach spaces E and F so that the k-adjoint of every linear operator/homogeneous polynomial from E to F belongs a given operator ideal I . Applications are provided for operators/polynomials on ℓ 1 and for the ideal of weakly compact operators. [ABSTRACT FROM AUTHOR]