Geodesic
Abstract Weyl-type theorems
Mathematica Bohemica, Tome 141 (2016) no. 4, pp. 495-508
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In this paper, we give a new approach to the study of Weyl-type theorems. Precisely, we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued functions, we reduce the question of relationship between Weyl-type theorems to the study of the set difference between the parts of the spectrum that are involved. This study solves completely the question of relationship between two spectral valued functions, comparable for one or the other order relation. Then several known results about Weyl-type theorems become corollaries of the results obtained.
In this paper, we give a new approach to the study of Weyl-type theorems. Precisely, we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued functions, we reduce the question of relationship between Weyl-type theorems to the study of the set difference between the parts of the spectrum that are involved. This study solves completely the question of relationship between two spectral valued functions, comparable for one or the other order relation. Then several known results about Weyl-type theorems become corollaries of the results obtained.
DOI : 10.21136/MB.2016.0046-14
Classification : 47A10, 47A11, 47A53
Keywords: spectral valued function; partitioning; spectrum; Weyl-type theorem 
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Berkani, Mohammed. Abstract Weyl-type theorems. Mathematica Bohemica, Tome 141 (2016) no. 4, pp. 495-508. doi: 10.21136/MB.2016.0046-14

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