Operators of Rank One in Reflexive Algebras
Operators of Rank One in Reflexive Algebras
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DOI：
10.4153/cjm-1976-003-1
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发表时间：
1976-02
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影响因子：
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通讯作者：
W. E. Longstaff
中科院分区：
文献类型：
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作者：
W. E. Longstaff
如果H是一个（复）Hilbert空间，并且是H的（闭线性）子空间的集合，则很容易证明作用在H上的所有（有界线性）算子的集合是一个包含恒等算子的弱闭算子代数。这个代数记作Alg。在这类代数的研究中，可以假设[4]是一个子空间格，即在任意交叉和任意（闭合线性）跨度的形成下是闭合的，并且包含零子空间（0）和H。这样的代数的类正是自反代数的类[3]。
If H is a (complex) Hilbert space and is a collection of (closed linear) subspaces of H it is easily shown that the set of all (bounded linear) operators acting on H which leave every member of invariant is a weakly closed operator algebra containing the identity operator. This algebra is denoted by Alg . In the study of such algebras it may be supposed [4] that is a subspace lattice i.e. that is closed under the formation of arbitrary intersections and arbitrary (closed linear) spans and contains both the zero subspace (0) and H. The class of such algebras is precisely the class of reflexive algebras [3].