Annals of Functional Analysis

Local Spectrum of a Family of Operators

Simona Macovei

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Abstract

‎Starting from the classic definitions of resolvent set and spectrum‎ ‎of a linear bounded operator on a Banach space‎, ‎we introduce the‎ ‎local resolvent set and local spectrum‎, ‎the local spectral space and‎ ‎the single-valued extension property of a family of linear bounded‎ ‎operators on a Banach space‎. ‎Keeping the analogy with the classic‎ ‎case‎, ‎we extend some of the known results from the case of a linear‎ ‎bounded operator to the case of a family of linear bounded operators‎ ‎on a Banach space.

Article information

Source
Ann. Funct. Anal., Volume 4, Number 2 (2013), 131-143.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399899531

Digital Object Identifier
doi:10.15352/afa/1399899531

Mathematical Reviews number (MathSciNet)
MR3034936

Zentralblatt MATH identifier
1287.47004

Subjects
Primary: 47A10: Spectrum, resolvent
Secondary: 47-01: Instructional exposition (textbooks, tutorial papers, etc.)

Keywords
Local spectrum local resolvent set ‎asymptotic ‎equivalence asymptotic qausinilpotent equivalence

Citation

Macovei, Simona. Local Spectrum of a Family of Operators. Ann. Funct. Anal. 4 (2013), no. 2, 131--143. doi:10.15352/afa/1399899531. https://projecteuclid.org/euclid.afa/1399899531


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References

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  • I. Colojoar and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breanch Science Publisher, 1968.
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  • S. Macovei, Spectrum of a Family of Operators, Surv. Math. Appl. 6 (2011), 137–159.