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Discontinuous Points of Nests and Some Ideals of Nest Algebras

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2009年05期
Page:
707-712
Research Field:
Publishing date:

Info

Title:
Discontinuous Points of Nests and Some Ideals of Nest Algebras
Author(s):
CHEN Pei-xin1LIU Jing-shuang2YANG Hong-ge1
1.School of Sciences,NUST,Nanjing 210094,China;2.Mathematical Science College,Baotou Teachers’ College,Baotou 014010,China
Keywords:
nests nest algebra two-order discintinuous points outer modules maximal(minimal) ideals
PACS:
O177.1
DOI:
-
Abstract:
Let N be a nest on a fixed linear norm space X,m(N) be the set of all maps of N into itself,put m0(N)={α∈m(N)α(0)=0,α is order preserving and left continuous}.For a subspace M,we first show that the following three statements are equivalent:(1)M is a weakly closed AlgN-module;(2)there exists α∈m0(N) such that M=Mα;(3)there exists β∈m(N) such that M=Mβ.If N contains 3 elements at most,the all weakly closed AlgN-modules can be listed;if N contains 4 elements at least,then the following statements are equivalent:(1)0<0+ and X-<X;(2)there exists minimal weakly closed idea of AlgN;(3)there exists maximal outer weakly closed AlgN-module.Moreover,suppose N be a non-trivial nest,then there exists discontinuous point in N if and only if there exists maximal weakly closed ideal of AlgN.Suppose N contain 4 elements at least,then there exists a two-order discontinuous point in N if and only if there exists minimal outer weakly closed AlgN-module.

References:

[ 1] Erdos JA, Power SC. Weakly closed ideals of nest algebras[ J]. JOperator Theory, 1982, 7: 219-235.
[ 2] LamoureuxM P. Nest representations and dynamical systems[ J]. JFunctAna,l 1993( 114): 467- 492.
[ 3] Orr JL. The maximal ideal of a nest algebra[ J]. JFuncAna,l 1994( 124): 119-134.
[ 4] Anoussis, KatsoulisM. A nonsel-f adjoint Russo-dye theorem[ J]. MathAnn, 1993( 304): 685- 699, MR97:f 47042.
[ 5] DavidsonK R. Nest Algebras, Triangular Forms for OperatorAlgebrasonHilbertSpaces[M]. NewYork: Longman, 1988.
[ 6] DavidsonKR. The Russo-dye theorem in nest alge-bras[ J]. Proc Amer Math Soc, 1998, 126( 10): 3055- 3059.
[ 7] Wu Jing. Local derivations of reflexive algebrasÒ [ J]. ProcAmerMathSoc, 2001, 129(6): 1933-1937.
[ 8] GongWeibang, Zhu Jun. Strong-principal bimodules ofnest algebras[ J] ProcAmerMathSoc, 1992, 115: 435-440.
[ 9] LongstaffWE. Strongly reflexive lattices[ J]. JLon-donMathSoc, 1975, 11( 2): 491- 498.
[ 10] SpanoudakisNK. Generalizationsof certainnest algebra results[ J]. ProcAmerMathSoc, 1992, 115: 711-723.
[ 11] Kraus J, LarsonDR. Reflexivity anddistance formula [ J]. ProcLondonMathSoc, 1986, 53(3): 340-356.
[ 12] Erdos JA. Operators of finite rank in nest algebras [ J]. JLondonMathSoc, 1968, 43: 391-397.
[ 13] Erdos JA. Reflexivity for subspacemaps and linear subspacesof operators[ J]. Proc LondonMathSoc, 1986, 52( 3): 582- 600.
[ 14] KnowlesG J. Onstructure of certainnest algebramod-ules[ J]. CanJMath, 1987,( 6): 1405-1412.

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Last Update: 2012-11-19