迁移算子的稠密性pHaar酉元及KS代数.pdfVIP

Æ ℄ B (H ) ℄ H . , Kadison B (H ) Æ . Arveson [1] A B (H ) , A Æ , A B (H ) . Kadison . [6] U. Haagerup H. Schultz  , Fang, Hadwin Ravichandran [4] . Π1 . , p − Haar Kadison-Singer . : , . G = {e, u }, u2 = e, i ∈ N , G = ∗ G {G : i ∈ N} , L(G) i i i i∈N i i ′ , R(G) = L(G) . , {λu1u2 + λu3u4 , λu5u6 + λu7u8 } R(G) B (H ) , {λu1u2 , λu3u4 } R(G) B (H ) . , p −Haar ∗ Æ ∗ , Mn (C) n − Haar . , CI Kadison-Singer , Kadison-Singer . : ; ; ; ; Π1 ; ; Æ; ∗ ; p − Haar ; Kadison-Singer ; Kadison-Singer ; . i Æ Abstract We denote by B(H) the algebra of all bounded linear operators on a Hilbert space H . With regards to the transitive algebra question. Kadison suggested the idea that some self-adjoint maximal abelian subalgebra of B(H) and some elements not in the subalgebra might generate a non-trivial transitive algebra. Arveson proved in [1] that Kadison’s original idea does not work. That is, if A is a transitive subalgebra of B(H) which contains a self-adjoint maximal abelian von Neumann algebra, then A is strong- operator dense in B(H). Inspired by the invariant subspace problem affiliated with a von Neumann algebra [6], Fang, Hadwin and Ravichandran [4] studied the transitive algebra generated by some set of operators in a finite von Neumann algebra and its commutant. we study the transitivity in a factor