Some spectral domain in approximate point-spectrum-preserving maps on B ( X ) $\mathcal {B}(\mathcal {X})$
Abstract Let X $\mathcal {X}$ be an infinite-dimensional complex Banach space, B ( X ) $\mathcal {B}(\mathcal {X})$ the algebra of all bounded linear operators on X $\mathcal {X}$ . Denote the spectral domain by σ γ ( T ) = { λ ∈ σ a ( T ) : T that is semi-Fredholm and a s c ( T − λ I ) < ∞ } $...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-08-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-023-03014-z |
| _version_ | 1797555739386970112 |
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| author | Ying Wang |
| author_facet | Ying Wang |
| author_sort | Ying Wang |
| collection | DOAJ |
| description | Abstract Let X $\mathcal {X}$ be an infinite-dimensional complex Banach space, B ( X ) $\mathcal {B}(\mathcal {X})$ the algebra of all bounded linear operators on X $\mathcal {X}$ . Denote the spectral domain by σ γ ( T ) = { λ ∈ σ a ( T ) : T that is semi-Fredholm and a s c ( T − λ I ) < ∞ } $\sigma _{\gamma}(T)=\{\lambda \in \sigma _{a}(T): T { \text{ that is semi-Fredholm and }} asc(T-\lambda I)<\infty \}$ . In this paper, we characterize the structure of additive surjective maps φ : B ( X ) → B ( X ) $\varphi : \mathcal {B}(\mathcal {X})\rightarrow \mathcal {B}(\mathcal {X})$ with σ γ ( φ ( T ) ) = σ γ ( T ) $\sigma _{\gamma}(\varphi (T))=\sigma _{\gamma}(T)$ for all T ∈ B ( X ) $T\in \mathcal{B(X)}$ . |
| first_indexed | 2024-03-10T16:51:45Z |
| format | Article |
| id | doaj.art-6038e10aa581409dafb623f42ba768ab |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-10T16:51:45Z |
| publishDate | 2023-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-6038e10aa581409dafb623f42ba768ab2023-11-20T11:16:06ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-08-01202311810.1186/s13660-023-03014-zSome spectral domain in approximate point-spectrum-preserving maps on B ( X ) $\mathcal {B}(\mathcal {X})$Ying Wang0China Academy of Space Technology (Xi’an)Abstract Let X $\mathcal {X}$ be an infinite-dimensional complex Banach space, B ( X ) $\mathcal {B}(\mathcal {X})$ the algebra of all bounded linear operators on X $\mathcal {X}$ . Denote the spectral domain by σ γ ( T ) = { λ ∈ σ a ( T ) : T that is semi-Fredholm and a s c ( T − λ I ) < ∞ } $\sigma _{\gamma}(T)=\{\lambda \in \sigma _{a}(T): T { \text{ that is semi-Fredholm and }} asc(T-\lambda I)<\infty \}$ . In this paper, we characterize the structure of additive surjective maps φ : B ( X ) → B ( X ) $\varphi : \mathcal {B}(\mathcal {X})\rightarrow \mathcal {B}(\mathcal {X})$ with σ γ ( φ ( T ) ) = σ γ ( T ) $\sigma _{\gamma}(\varphi (T))=\sigma _{\gamma}(T)$ for all T ∈ B ( X ) $T\in \mathcal{B(X)}$ .https://doi.org/10.1186/s13660-023-03014-zSpectral domainApproximate point spectrumAdditive preserver |
| spellingShingle | Ying Wang Some spectral domain in approximate point-spectrum-preserving maps on B ( X ) $\mathcal {B}(\mathcal {X})$ Journal of Inequalities and Applications Spectral domain Approximate point spectrum Additive preserver |
| title | Some spectral domain in approximate point-spectrum-preserving maps on B ( X ) $\mathcal {B}(\mathcal {X})$ |
| title_full | Some spectral domain in approximate point-spectrum-preserving maps on B ( X ) $\mathcal {B}(\mathcal {X})$ |
| title_fullStr | Some spectral domain in approximate point-spectrum-preserving maps on B ( X ) $\mathcal {B}(\mathcal {X})$ |
| title_full_unstemmed | Some spectral domain in approximate point-spectrum-preserving maps on B ( X ) $\mathcal {B}(\mathcal {X})$ |
| title_short | Some spectral domain in approximate point-spectrum-preserving maps on B ( X ) $\mathcal {B}(\mathcal {X})$ |
| title_sort | some spectral domain in approximate point spectrum preserving maps on b x mathcal b mathcal x |
| topic | Spectral domain Approximate point spectrum Additive preserver |
| url | https://doi.org/10.1186/s13660-023-03014-z |
| work_keys_str_mv | AT yingwang somespectraldomaininapproximatepointspectrumpreservingmapsonbxmathcalbmathcalx |