# Perturbation theory relative to a Banach algebra of operators

Studia Mathematica (1993)

- Volume: 106, Issue: 2, page 153-174
- ISSN: 0039-3223

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topBarnes, Bruce. "Perturbation theory relative to a Banach algebra of operators." Studia Mathematica 106.2 (1993): 153-174. <http://eudml.org/doc/216010>.

@article{Barnes1993,

abstract = {Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. Let S be a closed linear operator in X, and let R be a linear operator in X. In this paper the spectral and Fredholm theory relative to ℬ of the perturbed operator S + R is developed. In particular, the situation where R is S-inessential relative to ℬ is studied. Several examples are given to illustrate the usefulness of these concepts.},

author = {Barnes, Bruce},

journal = {Studia Mathematica},

keywords = {Banach algebra of operators; Fredholm operator; perturbation theory; essential spectrum; Fredholm theory; perturbed operator},

language = {eng},

number = {2},

pages = {153-174},

title = {Perturbation theory relative to a Banach algebra of operators},

url = {http://eudml.org/doc/216010},

volume = {106},

year = {1993},

}

TY - JOUR

AU - Barnes, Bruce

TI - Perturbation theory relative to a Banach algebra of operators

JO - Studia Mathematica

PY - 1993

VL - 106

IS - 2

SP - 153

EP - 174

AB - Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. Let S be a closed linear operator in X, and let R be a linear operator in X. In this paper the spectral and Fredholm theory relative to ℬ of the perturbed operator S + R is developed. In particular, the situation where R is S-inessential relative to ℬ is studied. Several examples are given to illustrate the usefulness of these concepts.

LA - eng

KW - Banach algebra of operators; Fredholm operator; perturbation theory; essential spectrum; Fredholm theory; perturbed operator

UR - http://eudml.org/doc/216010

ER -

## References

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- [10] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience, New York 1964.
- [11] S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York 1966.
- [12] K. Jörgens, Linear Integral Operators, Pitman, Boston 1982.
- [13] T. Kato, Perturbation Theory for Linear Operators, Springer, New York 1966.
- [14] D. Kleinecke, Almost-finite, compact, and inessential operators, Proc. Amer. Math. Soc. 14 (1963), 863-868.
- [15] R. Kress, Linear Integral Equations, Springer, Berlin 1989.
- [16] W. Pfaffenberger, On the ideals of strictly singular and inessential operators, Proc. Amer. Math. Soc. 25 (1970), 603-607.
- [17] M. Schechter, Principles of Functional Analysis, Academic Press, New York 1971.

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