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Czasopismo
1995 | 115 | 1 | 87-103
Tytuł artykułu

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

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
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.
Czasopismo
Rocznik
Tom
115
Numer
1
Strony
87-103
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-04-02
poprawiono
1995-02-10
Twórcy
  • Department of Mathematics, University of Oregon, Eugene, Oregon 97403, U.S.A.
Bibliografia
  • [A] C. Apostol, b*-algebras and their representation, J. London Math. Soc. 3 (1971), 30-38.
  • [B1] B. Barnes, Closed operators affiliated with a Banach algebra of operators, Studia Math. 101 (1992), 215-240.
  • [B2] B. Barnes, Perturbation theory relative to a Banach algebra of operators, ibid. 106 (1993), 153-174.
  • [BM] M. Boardman, Relative spectra in complete LMC-algebras with applications, Illinois J. Math. 39 (1995), 119-139.
  • [BD] F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973.
  • [DS] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience, New York, 1964.
  • [F] M. Fragoulopoulou, An Introduction to the Representation Theory of Topological *-Algebras, Schriftenreihe Math. Inst. Univ. Münster 48, 1988
  • [I] A. Inoue, Locally C*-algebras, Mem. Fac. Sci. Kyushu Univ. Ser. A 25 (1971), 197-235.
  • [J] K. Jörgens, Linear Integral Operators, Pitman, Boston, 1982.
  • [K] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
  • [KR] R. Kress, Linear Integral Equations, Springer, Berlin, 1989.
  • [PR] P. Patterson and T. Randolph, Semigroups affiliated with algebras of operators, Studia Math. 108 (1994), 87-102.
  • [R] C. Rickart, Banach Algebras, Van Nostrand, New York, 1960.
  • [S] K. Schmüdgen, Über LM C*-algebren, Math. Nachr. 68 (1975), 167-182.
  • [TL] A. Taylor and D. Lay, Introduction to Functional Analysis, 2nd ed., Wiley, New York, 1980.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv115i1p87bwm
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