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Tensor product of left n-invertible operators

B. P. DuggalVladimir Müller — 2013

Studia Mathematica

A Banach space operator T ∈ has a left m-inverse (resp., an essential left m-inverse) for some integer m ≥ 1 if there exists an operator S ∈ (resp., an operator S ∈ and a compact operator K ∈ ) such that i = 0 m ( - 1 ) i m i S m - i T m - i = 0 (resp., i = 0 m ( - 1 ) i m i T m - i S m - i = K ). If T i is left m i -invertible (resp., essentially left m i -invertible), then the tensor product T₁ ⊗ T₂ is left (m₁ + m₂-1)-invertible (resp., essentially left (m₁ + m₂-1)-invertible). Furthermore, if T₁ is strictly left m-invertible (resp., strictly essentially left m-invertible), then...

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