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A characterization of the essential spectrum and applications

Aref Jeribi (2002)

Bollettino dell'Unione Matematica Italiana

In this article the essential spectrum of closed, densely defined linear operators is characterized on a large class of spaces, which possess the Dunford-Pettis property or which isomorphic to one of the spaces L p Ω p > 1 . A practical...

A Class of Contractions in Hilbert Space and Applications

Nick Dungey (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1-β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup ( T ) n = 1 , 2 , . . . by the continuous semigroup ( e - t ( I - T ) ) t 0 . Moreover, we give a stronger quadratic form inequality which ensures that s u p n T - T n + 1 : n = 1 , 2 , . . . < . The results apply to large classes of Markov operators on countable spaces or on locally compact groups.

A la recherche du spectre perdu: An invitation to nonlinear spectral theory

Appell, Jürgen (2003)

Nonlinear Analysis, Function Spaces and Applications

We give a survey on spectra for various classes of nonlinear operators, with a particular emphasis on a comparison of their advantages and drawbacks. Here the most useful spectra are the asymptotic spectrum by M. Furi, M. Martelli and A. Vignoli (1978), the global spectrum by W. Feng (1997), and the local spectrum (called “phantom”) by P. Santucci and M. Väth (2000). In the last part we discuss these spectra for homogeneous operators (of any degree), and derive a discreteness result and a nonlinear...

A note on the a -Browder’s and a -Weyl’s theorems

M. Amouch, H. Zguitti (2008)

Mathematica Bohemica

Let T be a Banach space operator. In this paper we characterize a -Browder’s theorem for T by the localized single valued extension property. Also, we characterize a -Weyl’s theorem under the condition E a ( T ) = π a ( T ) , where E a ( T ) is the set of all eigenvalues of T which are isolated in the approximate point spectrum and π a ( T ) is the set of all left poles of T . Some applications are also given.

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