Tensor product of left n-invertible operators

B. P. Duggal, and Vladimir Müller. "Tensor product of left n-invertible operators." Studia Mathematica 215.2 (2013): 113-125. <http://eudml.org/doc/285583>.

@article{B2013,
abstract = {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 $∑_\{i=0\}^\{m\} (-1)^\{i\} \binom\{m\}\{i\} S^\{m-i\} T^\{m-i\} = 0$ (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).},
author = {B. P. Duggal, Vladimir Müller},
journal = {Studia Mathematica},
keywords = {Banach space; left n-invertible operator; essentially left -invertible operator; tensor product; left-right multiplication operator},
language = {eng},
number = {2},
pages = {113-125},
title = {Tensor product of left n-invertible operators},
url = {http://eudml.org/doc/285583},
volume = {215},
year = {2013},
}

TY - JOUR
AU - B. P. Duggal
AU - Vladimir Müller
TI - Tensor product of left n-invertible operators
JO - Studia Mathematica
PY - 2013
VL - 215
IS - 2
SP - 113
EP - 125
AB - 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 $∑_{i=0}^{m} (-1)^{i} \binom{m}{i} S^{m-i} T^{m-i} = 0$ (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).
LA - eng
KW - Banach space; left n-invertible operator; essentially left -invertible operator; tensor product; left-right multiplication operator
UR - http://eudml.org/doc/285583
ER -