设H1,H2,H3为无穷维复可分Hilbert空间,对给定关系A ∈ BR(H1),B ∈ BR(H2),C ∈ BR(H3),记MD,E,F=(A D E 0 B F 0 0 C)∈ BR(H1㊉ H2 ㊉ H3),给出了存在满足 D(0)⊆A(0),E(0)⊆A(0),F(0)⊆B(0)的 D∈ BR(H2,H1),E∈ BR(H3,H1),F ∈ BR(H3,H2)使得MD,E,F为Fredholm关系和Weyl关系的充分必要条件.
Abstract
Let H1,H2,H3 be infinite-dimensional complex separable Hilbert spaces,given the relation A∈ BR(H1),B ∈ BR(H2),C∈ BR(H3),and written MD,F,F=(A D E0 B F 0 0 C)∈BR(H1 ⊕ H2⊕ H3).Necessary and sufficient conditions are given for MD,E,F to be Fredholm relation and Weyl relations for some D∈ BR(H2,H1),E∈ BR(H3,H1),F∈ BR(H3,H2)with D(0)⊆A(0),E(0)⊆A(0),F(0)⊆B(0),respectively.
维普
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