Uncomplemented subspaces in operator and polynomial ideals

Generalizing a number of known linear and nonlinear results, we establish conditions for the space of linear operators belonging to a given operator ideal not to be complemented in the space of bounded linear operators, and for the space of n -homogeneous polynomials belonging to a given polynomial ideal not to be complemented in the space of continuous n -homogeneous polynomials. Illustrative examples are provided.