Communications in Mathematical Analysis

Essential Ascent of Closed Operator and Some Decomposition Theorems

Z. Garbouj and H. Skhiri

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Abstract

The aim of this work is to study the essential ascent and the related essential ascent spectrum of closed unbounded operators on a Banach space. Our approach is based on the concept of paracomplete subspaces of Banach spaces. We prove an unbounded spectral mapping theorem for the ascent spectrum and the essential ascent spectrum. A characterization of closed unbounded operators with finite essential ascent as direct sum of a suitable operators is proved. The new notion of a-essential index for closed unbounded operators with finite essential ascent is introduced. We also give some perturbations results for such operators. This paper extends some results proved in [1] to closed unbounded operators.

Article information

Source
Commun. Math. Anal., Volume 16, Number 2 (2014), 19-47.

Dates
First available in Project Euclid: 20 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1413810436

Mathematical Reviews number (MathSciNet)
MR3270575

Zentralblatt MATH identifier
1319.47010

Subjects
Primary: 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20]

Keywords
Paracomplete space closed unbounded operators spectrum ascent essentiel ascent descent essential descent semi-Fredholm operators index

Citation

Garbouj, Z.; Skhiri, H. Essential Ascent of Closed Operator and Some Decomposition Theorems. Commun. Math. Anal. 16 (2014), no. 2, 19--47. https://projecteuclid.org/euclid.cma/1413810436


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