For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^*; A is a hyper-generalized n. idempotent if A^n = A^+. The set of all n-idempotents, all gen...For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^*; A is a hyper-generalized n. idempotent if A^n = A^+. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In(H), gIn(H) and HgIn(H), respectively. In this note, we obtain a chain of proper inclusions gIn(H) belong to HgIn(H) belong to In+2(H).展开更多
Let M⊆B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weightτwhere B(H)is the set of all bounded linear operators on Hilbert space H.The main purpose of...Let M⊆B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weightτwhere B(H)is the set of all bounded linear operators on Hilbert space H.The main purpose of this article is to introduce generalized weak wave operators Wf_(±),generalized weak abelian wave operators ■ and generalized stationary wave operators U_(±) in M and then to explore the relation among W_(±),■,U_(±) and generalized wave operators W_(±).展开更多
文摘For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^*; A is a hyper-generalized n. idempotent if A^n = A^+. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In(H), gIn(H) and HgIn(H), respectively. In this note, we obtain a chain of proper inclusions gIn(H) belong to HgIn(H) belong to In+2(H).
基金Supported by the Undergraduate Training Program on Innovation and Entrepreneurship(Grant No.X202110251333)National Natural Science Foundation of China(Grant No.11671133).
文摘Let M⊆B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weightτwhere B(H)is the set of all bounded linear operators on Hilbert space H.The main purpose of this article is to introduce generalized weak wave operators Wf_(±),generalized weak abelian wave operators ■ and generalized stationary wave operators U_(±) in M and then to explore the relation among W_(±),■,U_(±) and generalized wave operators W_(±).