# Closed operators affiliated with a Banach algebra of operators

Studia Mathematica (1992)

- Volume: 101, Issue: 3, page 215-240
- ISSN: 0039-3223

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topBarnes, Bruce. "Closed operators affiliated with a Banach algebra of operators." Studia Mathematica 101.3 (1992): 215-240. <http://eudml.org/doc/215902>.

@article{Barnes1992,

abstract = {Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. If S is a closed operator in X such that (λ - S)^\{-1\} ∈ ℬ for some number λ, then S is affiliated with ℬ. The object of this paper is to study the spectral theory and Fredholm theory relative to ℬ of an operator which is affiliated with ℬ. Also, applications are given to semigroups of operators which are contained in ℬ.},

author = {Barnes, Bruce},

journal = {Studia Mathematica},

keywords = {closed operator; spectrum; Fredholm operator; semigroup of operators; Banach algebra; operators affiliated with a Banach algebra of operators; Banach algebra of bounded linear operators on a Banach space; semigroups of operators},

language = {eng},

number = {3},

pages = {215-240},

title = {Closed operators affiliated with a Banach algebra of operators},

url = {http://eudml.org/doc/215902},

volume = {101},

year = {1992},

}

TY - JOUR

AU - Barnes, Bruce

TI - Closed operators affiliated with a Banach algebra of operators

JO - Studia Mathematica

PY - 1992

VL - 101

IS - 3

SP - 215

EP - 240

AB - Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. If S is a closed operator in X such that (λ - S)^{-1} ∈ ℬ for some number λ, then S is affiliated with ℬ. The object of this paper is to study the spectral theory and Fredholm theory relative to ℬ of an operator which is affiliated with ℬ. Also, applications are given to semigroups of operators which are contained in ℬ.

LA - eng

KW - closed operator; spectrum; Fredholm operator; semigroup of operators; Banach algebra; operators affiliated with a Banach algebra of operators; Banach algebra of bounded linear operators on a Banach space; semigroups of operators

UR - http://eudml.org/doc/215902

ER -

## References

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- [11] K. Jörgens, Linear Integral Operators, Pitman, Boston 1982.
- [12] R. Kress, Linear Integral Equations, Springer, Berlin 1989.
- [13] G. Lumer and R. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961), 679-698.
- [14] R. Nagel et al., One-parameter Semigroups of Positive Operators, Lecture Notes in Math. 1184, Springer, Berlin 1986.
- [15] M. Schechter, Principles of Functional Analysis, Academic Press, New York 1971.

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