Acta mathematica scientia, Series B >
SPECTRAL MAPPING THEOREM FOR ASCENT, ESSENTIAL ASCENT, DESCENT AND ESSENTIAL DESCENT SPECTRUM OF LINEAR RELATIONS
Received date: 2012-12-13
Revised date: 2013-09-11
Online published: 2014-07-20
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
Ezzeddine CHAFAI , Maher MNIF . SPECTRAL MAPPING THEOREM FOR ASCENT, ESSENTIAL ASCENT, DESCENT AND ESSENTIAL DESCENT SPECTRUM OF LINEAR RELATIONS[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1212 -1224 . DOI: 10.1016/S0252-9602(14)60080-1
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