Closed operators affiliated with a Banach algebra of operators

Bruce Barnes

Studia Mathematica (1992)

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

Abstract

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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.

How to cite

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Barnes, 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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  8. [8] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience, New York 1964. 
  9. [9] S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York 1966. Zbl0148.12501
  10. [10] E. Hille and R. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc., Providence 1957. Zbl0078.10004
  11. [11] K. Jörgens, Linear Integral Operators, Pitman, Boston 1982. 
  12. [12] R. Kress, Linear Integral Equations, Springer, Berlin 1989. 
  13. [13] G. Lumer and R. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961), 679-698. Zbl0101.09503
  14. [14] R. Nagel et al., One-parameter Semigroups of Positive Operators, Lecture Notes in Math. 1184, Springer, Berlin 1986. Zbl0585.47030
  15. [15] M. Schechter, Principles of Functional Analysis, Academic Press, New York 1971. Zbl0211.14501

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