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1994 | 111 | 3 | 223-239
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Operators in finite distributive subspace lattices II

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EN
Abstrakty
EN
In a previous paper we gave an example of a finite distributive subspace lattice ℒ on a Hilbert space and a rank two operator of Algℒ that cannot be written as a finite sum of rank one operators from Algℒ. The lattice ℒ was a specific realization of the free distributive lattice on three generators. In the present paper, which is a sequel to the aforementioned one, we study Algℒ for the general free distributive lattice with three generators (on a normed space). Necessary and sufficient conditions are given for 1) a finite rank operator of Algℒ to be written as a finite sum of rank ones from Algℒ, and 2) a realization of ℒ to contain a finite rank operator of Algℒ with the preceding property. These results are then used to show the curiosity that the product of two finite rank operators of Algℒ always has the above property.
Słowa kluczowe
Czasopismo
Rocznik
Tom
111
Numer
3
Strony
223-239
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-11-25
poprawiono
1994-02-25
Twórcy
  • Department of Mathematics, University of Crete, 714 09, Iraklion Crete, Greece
Bibliografia
  • [1] J. A. Erdos, Operators of finite rank in nest algebras, J. London Math. Soc. 43 (1968), 391-397.
  • [2] A. Hopenwasser and R. Moore, Finite rank operators in reflexive operator algebras, J. London Math. Soc. (2) 27 (1983), 331-338.
  • [3] M. S. Lambrou, Approximants, commutants and double commutants in normed algebras, ibid. 25 (1982), 499-512.
  • [4] W. E. Longstaff, Strongly reflexive lattices, ibid. 11 (1975), 491-498.
  • [5] W. E. Longstaff, Operators of rank one in reflexive algebras, Canad. J. Math. 28 (1976), 19-23.
  • [6] N. K. Spanoudakis, Generalizations of certain nest algebra results, Proc. Amer. Math. Soc. 115 (1992), 711-723.
  • [7] N. K. Spanoudakis, Operators in finite distributive subspace lattices I, Math. Proc. Cambridge Philos. Soc. 113 (1993), 141-146.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv111i3p223bwm
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