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Tensor product of left n-invertible operators

100%

Duggal B., Müller V.

Studia Mathematica

2013

tom 215

nr 2

113-125

A Banach space operator T ∈ 𝒳 has a left m-inverse (resp., an essential left m-inverse) for some integer m ≥ 1 if there exists an operator S ∈ 𝒳 (resp., an operator S ∈ 𝒳 and a compact operator K ∈ 𝒳) such that $∑_{i=0}^{m} (-1)^{i} \binom{m}{i} S^{m-i} T^{m-i} = 0$ (resp., $∑_{i=0}^{m} (-1)^{i} \binom{m}{i} T^{m-i} S^{m-i} = K$). 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 T₁ ⊗ T₂ is: (i) left (m + n - 1)-invertible (resp., essentially left (m + n - 1)-invertible) if and only if T₂ is left n-invertible (resp., essentially left n-invertible); (ii) strictly left (m + n - 1)-invertible (resp., strictly essentially left (m + n - 1)-invertible) if and only if T₂ is strictly left n-invertible (resp., strictly essentially left n-invertible).

On Jordan models of $C_0$-contractions

60%

Müller V.

Banach Center Publications

1982

tom 8

nr 1

353-354

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Müller V.

1 Duggal B.

1 2013

1 1982

Wyniki wyszukiwania

Tensor product of left n-invertible operators

On Jordan models of $C_0$-contractions