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 |
| Summary: | 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 ) $T\in \mathcal{B(X)}$ . |
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| ISSN: | 1029-242X |