On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility
A generalisation of m-expansive Hilbert space operators T ∈ B(ℋ) [18, 20] to Banach space operators T ∈ B(𝒳) is obtained by defining that a pair of operators A, B ∈ B(𝒳) is (m, P)-expansive for some operator P ∈ B(𝒳) if Δ A,Bm(P)= (I-LARB)m(P)=∑j=0m(-1)j(jm){\left( {I - {L_A}{R_B}} \right)^m}\left(...
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De Gruyter
2021
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oai:doaj.org-article:67e6529f69654bfe9bc74d2146fcb1d92021-12-05T14:10:45ZOn (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility2299-328210.1515/conop-2020-0120https://doaj.org/article/67e6529f69654bfe9bc74d2146fcb1d92021-11-01T00:00:00Zhttps://doi.org/10.1515/conop-2020-0120https://doaj.org/toc/2299-3282A generalisation of m-expansive Hilbert space operators T ∈ B(ℋ) [18, 20] to Banach space operators T ∈ B(𝒳) is obtained by defining that a pair of operators A, B ∈ B(𝒳) is (m, P)-expansive for some operator P ∈ B(𝒳) if Δ A,Bm(P)= (I-LARB)m(P)=∑j=0m(-1)j(jm){\left( {I - {L_A}{R_B}} \right)^m}\left( P \right) = \sum\nolimits_{j = 0}^m {{{\left( { - 1} \right)}^j}\left( {_j^m} \right)}AjPBj≤0; LA(X) = AX and RB(X)=XB.Duggal B.P.De Gruyterarticlehilbert/banach spaceleft/right multiplication operator(m, p)-expansive operatorsm-left invertible/m-isometric operatorsproduct of operatorsperturbation by nilpotentsdrazin invertible operators47a05, 47a55secondary 47a11, 47b47MathematicsQA1-939ENConcrete Operators, Vol 8, Iss 1, Pp 158-175 (2021) |
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DOAJ |
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DOAJ |
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EN |
| topic |
hilbert/banach space left/right multiplication operator (m, p)-expansive operators m-left invertible/m-isometric operators product of operators perturbation by nilpotents drazin invertible operators 47a05, 47a55 secondary 47a11, 47b47 Mathematics QA1-939 |
| spellingShingle |
hilbert/banach space left/right multiplication operator (m, p)-expansive operators m-left invertible/m-isometric operators product of operators perturbation by nilpotents drazin invertible operators 47a05, 47a55 secondary 47a11, 47b47 Mathematics QA1-939 Duggal B.P. On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility |
| description |
A generalisation of m-expansive Hilbert space operators T ∈ B(ℋ) [18, 20] to Banach space operators T ∈ B(𝒳) is obtained by defining that a pair of operators A, B ∈ B(𝒳) is (m, P)-expansive for some operator P ∈ B(𝒳) if Δ A,Bm(P)= (I-LARB)m(P)=∑j=0m(-1)j(jm){\left( {I - {L_A}{R_B}} \right)^m}\left( P \right) = \sum\nolimits_{j = 0}^m {{{\left( { - 1} \right)}^j}\left( {_j^m} \right)}AjPBj≤0; LA(X) = AX and RB(X)=XB. |
| format |
article |
| author |
Duggal B.P. |
| author_facet |
Duggal B.P. |
| author_sort |
Duggal B.P. |
| title |
On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility |
| title_short |
On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility |
| title_full |
On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility |
| title_fullStr |
On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility |
| title_full_unstemmed |
On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility |
| title_sort |
on (m, p)-expansive operators: products, perturbation by nilpotents, drazin invertibility |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/67e6529f69654bfe9bc74d2146fcb1d9 |
| work_keys_str_mv |
AT duggalbp onmpexpansiveoperatorsproductsperturbationbynilpotentsdrazininvertibility |
| _version_ |
1718371763306364928 |