数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (5): 1437-1452.doi: 10.1016/S0252-9602(17)30083-8

• 论文 • 上一篇    下一篇

LEFT-RIGHT BROWDER LINEAR RELATIONS AND RIESZ PERTURBATIONS

Teresa ÁLVAREZ   

  1. Department of Mathematics, University of Oviedo, 33007, Oviedo, Asturias, Spain
  • 收稿日期:2015-11-06 修回日期:2016-11-25 出版日期:2017-10-25 发布日期:2017-10-25
  • 作者简介:Teresa ÁLVAREZ,E-mail:seco@uniovi.es
  • 基金资助:

    Supported by MICINN (Spain) Grant MTM2013-45643.

LEFT-RIGHT BROWDER LINEAR RELATIONS AND RIESZ PERTURBATIONS

Teresa ÁLVAREZ   

  1. Department of Mathematics, University of Oviedo, 33007, Oviedo, Asturias, Spain
  • Received:2015-11-06 Revised:2016-11-25 Online:2017-10-25 Published:2017-10-25
  • Supported by:

    Supported by MICINN (Spain) Grant MTM2013-45643.

摘要:

A closed linear relation T in a Banach space X is called left (resp. right) Fredholm if it is upper (resp. lower) semiFredholm and its range (resp. null space) is topologically complemented in X. We say that T is left (resp. right) Browder if it is left (resp. right) Fredholm and has a finite ascent (resp. descent). In this paper, we analyze the stability of the left (resp. right) Fredholm and the left (resp. right) Browder linear relations under commuting Riesz operator perturbations. Recent results of Zivkovic et al. to the case of bounded operators are covered.

关键词: left and right Fredholm linear relations, left and right Browder linear relations, Riesz perturbations

Abstract:

A closed linear relation T in a Banach space X is called left (resp. right) Fredholm if it is upper (resp. lower) semiFredholm and its range (resp. null space) is topologically complemented in X. We say that T is left (resp. right) Browder if it is left (resp. right) Fredholm and has a finite ascent (resp. descent). In this paper, we analyze the stability of the left (resp. right) Fredholm and the left (resp. right) Browder linear relations under commuting Riesz operator perturbations. Recent results of Zivkovic et al. to the case of bounded operators are covered.

Key words: left and right Fredholm linear relations, left and right Browder linear relations, Riesz perturbations