Consistent in invertibility operators and SVEP

Abstract

If S(X) ⊂ B(X), where B(X) denotes the algebra of operators on a Banach space X, then A ∈ B(X) is S(X) consistent if AB ∈ S(X) ⇐⇒ BA ∈ S(X) for every B ∈ B(X). SVEP is a powerful tool in determining the S(X) consistency of operators A for various choices of the subset S(X).