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Some facts from descriptive set theory concerning essential spectra and applications

Khalid Latrach, J. Martin Paoli, Pierre Simonnet (2005)

Studia Mathematica

Let X be a separable Banach space and denote by 𝓛(X) (resp. 𝒦(ℂ)) the set of all bounded linear operators on X (resp. the set of all compact subsets of ℂ). We show that the maps from 𝓛(X) into 𝒦(ℂ) which assign to each element of 𝓛(X) its spectrum, approximate point spectrum, essential spectrum, Weyl essential spectrum, Browder essential spectrum, respectively, are Borel maps, where 𝓛(X) (resp. 𝒦(ℂ)) is endowed with the strong operator topology (resp. Hausdorff topology). This enables us...

Some families of pseudo-processes

J. Kłapyta (1994)

Annales Polonici Mathematici

We introduce several types of notions of dis persive, completely unstable, Poisson unstable and Lagrange uns table pseudo-processes. We try to answer the question of how many (in the sense of Baire category) pseudo-processes with each of these properties can be defined on the space m . The connections are discussed between several types of pseudo-processes and their limit sets, prolongations and prolongational limit sets. We also present examples of applications of the above results to pseudo-processes...

Some Fixed Point Theorems for Kannan Mappings

Tejpal, Shavetambry, Narang, T. D. (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.Some results on the existence and uniqueness of fixed points for Kannan mappings on admissible subsets of bounded metric spaces and on bounded closed convex subsets of complete convex metric spaces having uniform normal structure are proved in this paper. These results extend and generalize some results of Ismat Beg and Akbar Azam [Ind. J. Pure Appl. Math. 18 (1987), 594-596], A. A. Gillespie and B. B. Williams [J. Math. Anal....

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