【摘要】：令H是維數(shù)大于2的復(fù)Hilbert空間,A是H上自伴標(biāo)準(zhǔn)算子代數(shù).對(duì)于給定的正整數(shù)κ≥1,H上算子A與B的κ-斜交換子遞推地定義為_(kāi)*[A,B]_κ=_*[A,_*[A,B]_(k-1)],其中_*[A,B]_0=B,_*[A,B]_1=AB-BA~*.設(shè)κ≥4,φ是A上的值域包含所有一秩投影的映射.本文證明了φ滿足_*[φ(A),φ(B)]_κ=_*[A,B]_κ對(duì)任意A,B∈A都成立的充分必要條件是φ(A)=A對(duì)任意A∈A都成立,或φ(A)=-A對(duì)任意A∈A都成立,當(dāng)κ是偶數(shù)時(shí)后一情形不出現(xiàn).
[Abstract]:Let H be a complex Hilbert space with dimensions greater than 2 and A be a self-adjoint standard operator algebra on H. For a given positive integer 魏 鈮，

本文編號(hào)：2173561