Operator Ideals Generalizing the Ideal of Strictly Singular Operators

Abstract

Abstract It is well‐known that an operator T ∈ L( E, F ) is strictly singular if ∥ T x ∥≧λ∥ x ∥ on a subspace Z ⊂ E implies dim Z < + ∞. The present paper deals with ideals of operators defined by a condition — ∥ T x ∥≧λ∥ x ∥ on an infinite‐dimensional subspace Z ⊂ E implies Z ∉ F — F being a „quasi‐injective”︁ class of BANACH spaces.