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1991 | 100 | 3 | 219-228
Tytuł artykułu

Korovkin theory in normed algebras

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
If A is a normed power-associative complex algebra such that the selfadjoint part is normally ordered with respect to some order, then the Korovkin closure (see the introduction for definitions) of T ∪ {t* ∘ t| t ∈ T} contains J*(T) for any subset T of A. This can be applied to C*-algebras, minimal norm ideals on a Hilbert space, and to H*-algebras. For bounded H*-algebras and dual C*-algebras there is even equality. This answers a question posed in [1].
Słowa kluczowe
Czasopismo
Rocznik
Tom
100
Numer
3
Strony
219-228
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-05-28
poprawiono
1991-04-25
Twórcy
  • Mathematisches Institut, Universität Münster, Einsteinstraße 62, 4400 Münster, Germany
Bibliografia
  • [1] F. Altomare, Korovkin closures in Banach algebras, in: Advances in Invariant Subspaces and Other Results of Operator Theory, Proc. 9th Internat. Conf. on Operator Theory, Timișoara and Herculane 1984, Oper. Theory: Adv. Appl. 17, Birkhäuser, Basel 1986, 35-42.
  • [2] W. Ambrose, Structure theorems for a special class of Banach algebras, Trans. Amer. Math. Soc. 57 (1945), 364-386.
  • [3] F. Beckhoff, Korovkin-Theory in Algebren, Schriftenreihe Math. Inst. Univ. Münster, Ser. 2, Heft 45, 1987.
  • [4] F. Beckhoff, A counterexample in Korovkin theory, Rend. Circ. Mat. Palermo (2) 37 (1988), 469-473.
  • [5] O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer, Berlin 1979.
  • [6] J. Dixmier, Von Neumann Algebras, North-Holland Math. Library 27, 1981.
  • [7] N. Dunford and J. T. Schwartz, Linear Operators II, Interscience Publ., 1963.
  • [8] R. V. Kadison, A generalized Schwarz inequality and algebraic invariants of operator algebras, Ann. of Math. 56 (1952), 494-503.
  • [9] I. Kaplansky, Groups with representations of bounded degree, Canad. J. Math. 1 (1949), 105-112.
  • [10] B. V. Limaye and M. N. N. Namboodiri, Korovkin approximation on C*-algebras, J. Approx. Theory 34 (1982), 237-246.
  • [11] B. V. Limaye and M. N. N. Namboodiri, Weak Korovkin approximation by completely positive linear maps on β(H), ibid. 42 (1984), 201-211.
  • [12] B. V. Limaye and M. N. N. Namboodiri, Weak approximation by positive maps on C*-algebras, to appear.
  • [13] L. H. Loomis, An Introduction to Abstract Harmonic Analysis, D. van Nostrand, New York 1953.
  • [14] M. Pannenberg, Korovkin approximation in Waelbroeck algebras, Math. Ann. 274 (1986), 423-437.
  • [15] W. M. Priestley, A noncommutative Korovkin theorem, J. Approx. Theory 16 (1976), 251-260.
  • [16] A. G. Robertson, A Korovkin theorem for Schwarz maps on C*-algebras, Math. Z. 56 (1977), 205-207.
  • [17] R. Schatten, Norm Ideals of Completely Continuous Operators, Springer, Berlin 1960.
  • [18] M. Takesaki, Theory of Operator Algebras I, Springer, New York 1979.
  • [19] B. Yood, Hilbert algebras as topological algebras, Ark. Mat. 12 (1974), 131-151.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv100i3p219bwm
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