= Strictly singular operator
A bounded linear operator is strictly singular if it is bounded below on no infinite-dimensional subspace. Equivalently, every infinite-dimensional subspace contains unit vectors with arbitrarily small images. On a <hereditarily indecomposable Banach space>, an operator which is arbitrarily small on unit vectors in every finite-codimensional subspace is strictly singular: construct an infinite basic span on which its operator norm is small, then use the zero-angle property of hereditary indecomposability.
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