数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1212-1224.doi: 10.1016/S0252-9602(14)60080-1

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SPECTRAL MAPPING THEOREM FOR ASCENT, ESSENTIAL ASCENT, DESCENT AND ESSENTIAL DESCENT SPECTRUM OF LINEAR RELATIONS

Ezzeddine CHAFAI|Maher MNIF   

  1. Departement of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Tunisia
  • 收稿日期:2012-12-13 修回日期:2013-09-11 出版日期:2014-07-20 发布日期:2014-07-20

SPECTRAL MAPPING THEOREM FOR ASCENT, ESSENTIAL ASCENT, DESCENT AND ESSENTIAL DESCENT SPECTRUM OF LINEAR RELATIONS

Ezzeddine CHAFAI|Maher MNIF   

  1. Departement of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Tunisia
  • Received:2012-12-13 Revised:2013-09-11 Online:2014-07-20 Published:2014-07-20

摘要:

In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a vector space to linear relations acting on Banach spaces. We focus to define and study the descent, essential descent, ascent and essential ascent spectrum of a linear relation everywhere defined on a Banach space X. In particular, we show that the corresponding spectrum satisfy the polynomial version of the spectral mapping theorem.

关键词: ascent, essential ascent, descent, essential descent, linear relations

Abstract:

In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a vector space to linear relations acting on Banach spaces. We focus to define and study the descent, essential descent, ascent and essential ascent spectrum of a linear relation everywhere defined on a Banach space X. In particular, we show that the corresponding spectrum satisfy the polynomial version of the spectral mapping theorem.

Key words: ascent, essential ascent, descent, essential descent, linear relations

中图分类号: 

  • 47A06