Abstract Weyl-type theorems

Mohammed Berkani

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 4, page 495-508
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Berkani, Mohammed. "Abstract Weyl-type theorems." Mathematica Bohemica 141.4 (2016): 495-508. <http://eudml.org/doc/287574>.

@article{Berkani2016,
abstract = {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.},
author = {Berkani, Mohammed},
journal = {Mathematica Bohemica},
keywords = {spectral valued function; partitioning; spectrum; Weyl-type theorem},
language = {eng},
number = {4},
pages = {495-508},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Abstract Weyl-type theorems},
url = {http://eudml.org/doc/287574},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Berkani, Mohammed
TI - Abstract Weyl-type theorems
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 4
SP - 495
EP - 508
AB - 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.
LA - eng
KW - spectral valued function; partitioning; spectrum; Weyl-type theorem
UR - http://eudml.org/doc/287574
ER -

References

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