Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras

Bruce Barnes

Studia Mathematica (1995)

  • Volume: 115, Issue: 1, page 87-103
  • ISSN: 0039-3223

Abstract

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The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.

How to cite

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Barnes, Bruce. "Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras." Studia Mathematica 115.1 (1995): 87-103. <http://eudml.org/doc/216200>.

@article{Barnes1995,
abstract = {The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.},
author = {Barnes, Bruce},
journal = {Studia Mathematica},
keywords = {convergence in the generalized sense; spectral theory; LMC-algebra; closed operators; affiliated with a Banach algebra of operators},
language = {eng},
number = {1},
pages = {87-103},
title = {Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras},
url = {http://eudml.org/doc/216200},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Barnes, Bruce
TI - Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 1
SP - 87
EP - 103
AB - The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.
LA - eng
KW - convergence in the generalized sense; spectral theory; LMC-algebra; closed operators; affiliated with a Banach algebra of operators
UR - http://eudml.org/doc/216200
ER -

References

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  1. [A] C. Apostol, b*-algebras and their representation, J. London Math. Soc. 3 (1971), 30-38. 
  2. [B1] B. Barnes, Closed operators affiliated with a Banach algebra of operators, Studia Math. 101 (1992), 215-240. Zbl0816.47002
  3. [B2] B. Barnes, Perturbation theory relative to a Banach algebra of operators, ibid. 106 (1993), 153-174. Zbl0810.47009
  4. [BM] M. Boardman, Relative spectra in complete LMC-algebras with applications, Illinois J. Math. 39 (1995), 119-139. Zbl0833.46033
  5. [BD] F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973. Zbl0271.46039
  6. [DS] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience, New York, 1964. 
  7. [F] M. Fragoulopoulou, An Introduction to the Representation Theory of Topological *-Algebras, Schriftenreihe Math. Inst. Univ. Münster 48, 1988 Zbl0653.46058
  8. [I] A. Inoue, Locally C*-algebras, Mem. Fac. Sci. Kyushu Univ. Ser. A 25 (1971), 197-235. 
  9. [J] K. Jörgens, Linear Integral Operators, Pitman, Boston, 1982. Zbl0499.47029
  10. [K] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966. Zbl0148.12601
  11. [KR] R. Kress, Linear Integral Equations, Springer, Berlin, 1989. 
  12. [PR] P. Patterson and T. Randolph, Semigroups affiliated with algebras of operators, Studia Math. 108 (1994), 87-102. Zbl0821.47033
  13. [R] C. Rickart, Banach Algebras, Van Nostrand, New York, 1960. 
  14. [S] K. Schmüdgen, Über LM C*-algebren, Math. Nachr. 68 (1975), 167-182. 
  15. [TL] A. Taylor and D. Lay, Introduction to Functional Analysis, 2nd ed., Wiley, New York, 1980. 

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