Tensor product of left n-invertible operators

• Autorzy: B. P. Duggal , Vladimir Müller
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 47A80: Tensor products of operators
• 47B47: Commutators, derivations, elementary operators, etc.
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 215
• Numer: 2
• Strony: 113-125

Daty

wydano

2013

Twórcy

autor

B. P. Duggal

• 8 Redwood Grove, Northfield Avenue, London W5 4SZ, England, U.K.

autor

Vladimir Müller

• Institute of Mathematics AV ČR, Žitnà25, 11567 Praha 1, Czech Republic

Identyfikatory

DOI

10.4064/sm215-2-2