Condition spectra of special operators and condition spectra preservers

Pseudospectra of Special Operators and Pseudosectrum Preservers

Denote by B(H) the Banach algebra of all bounded linear operators on a complex Hilbert space H. Let A ∈ B(H), and denote by σ(A) the spectrum of A. For ε > 0, define the ε-pseudospectrum σε(A) of A as σε(A) = {z ∈ σ(A+ E) : E ∈ B(H), ∥E∥ < ε}. In this paper, the pseudospectra of several special classes of operators are characterized. As an application, complete descriptions are given of the map...

Stability of essential spectra of bounded linear operators

In this paper‎, ‎we show the stability of Gustafson‎, ‎Weidmann‎, ‎Kato‎, ‎Wolf‎, ‎Schechter and Browder essential spectrum of bounded linear operators on Banach spaces which remain invariant under additive perturbations‎ ‎belonging to a broad classes of operators $U$ such $gamma(U^m)

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

Examples of operators and spectra

[1.0.2] Remark: The same argument applied to T shows that σ(T) is inside the closed ball of radius |T|op. By the elementary identity T − λ = (T − λ) · (Tn−1 + Tn−2λ+ . . .+ Tλn−2 + λn−2) (T − λ)−1 exists for |λ| > |T|op, that is, for |λ| > |Tn| op . That is, σ(T ) is inside the closed ball of radius infn≥1 |Tn| op . The latter expression is the spectral radius of T . This notion is relevant to ...

Linear Operators and Their Spectra