Factorisation in nest algebras
نویسندگان
چکیده
منابع مشابه
Triangular Algebras and Ideals of Nest Algebras
Let %? be a separable Hubert space and !T c 3§(J%f) be an algebra of bounded operators. Say F is triangular if ^ n ^ * is a maximal abelian self-adjoint subalgebra (m.a.s.a.) of 3B{%?) and call this m.a.s.a. the diagonal of J7". A triangular algebra is maximal triangular if it is not properly contained in any triangular algebra. Triangular algebras of operators have been studied for 30 years no...
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We consider the factorisation problem for bialgebras: when a bialgebraK factorises as K = HL, where H and L are algebras and coalgebras (but not necessarily bialgebras). Given two maps R : H ⊗ L → L ⊗H and W : L ⊗H → H ⊗ L, we introduce a product L W⊲⊳R H , and we give necessary and sufficient conditions for L W⊲⊳R H to be a bialgebra. It turns out that K factorises as K = HL if and only if K ∼...
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Let X and Y be operators on Hilbert space, and let L be a nest of projections on the space. We consider the problem of finding an operator A in Alg L: such that A is Hilbert-Schmidt and such that AX = Y. A necessary and sufficient condition involving X,Y, and the projections in the lattice is found. We also indicate how the statements of the results can be modified so that the main theorem is t...
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We shall show that B(H) can be represented by the strong closure of the linear span of the compounds of a fixed operator in B(H) and the rank one operators, composed only by the vectors of a certain orthonormal basis of H, in a nest algebra, even, under some assumption, in the radical of a nest algebra. 0. Notations, basic relationships, and introduction Throughout, the nonzero Hilbert space H ...
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We establish a general result about extending a right invertible row over a Banach algebra to an invertible matrix. This is applied to the computation of right topological stable rank of a split exact sequence. We also introduce a quantitative measure of stable rank. These results are applied to compute the right (left) topological stable rank for all nest algebras. This value is either 2 or in...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03430-8