We discuss the properties of an ordinal consistency matrix on the base of its directed graph, which benefit deriving the ranking of the compared alternatives.
Let (G, E) be a quasi-ordered group such that E∩E -1 is infinite, (G, G +) an ordered group with G +EG, and (G, G 1) the partially ordered group induced by (G, E).Let γ E, G + ∶T G + →T E and γ E, G 1 ∶T G 1 →T E be the corresponding natural morphisms between Toeplitz algebras. We prove that the kernel Ker γ E, G + is rigid,while Ker γ E, G 1 is equal to the compact-operator ideal on 2(G 1), and all Fredholm operators in the Toeplitz algebra T G 1 are of index zero.
The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule containing the nest algebra. They also prove that Hcb^n（A, M） ≌ Hcb^n（A, M） for all n ≥ 1 and a CSL algebra .A with an ultraweakly closed .A-bimodul.M containing A.
