کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416288 | 1631127 | 2015 | 20 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Maps preserving peripheral spectrum of generalized products of operators Maps preserving peripheral spectrum of generalized products of operators](/preview/png/6416288.png)
Let A1 and A2 be standard operator algebras on complex Banach spaces X1 and X2, respectively. For k⩾2, let (i1,â¦,im) be a sequence with terms chosen from {1,â¦,k}, and assume that at least one of the terms in (i1,â¦,im) appears exactly once. Define the generalized product T1âT2ââ¯âTk=Ti1Ti2â¯Tim on elements in Ai. Let Φ:A1âA2 be a map with the range containing all operators of rank at most two. We show that Φ satisfies that ÏÏ(Φ(A1)ââ¯âΦ(Ak))=ÏÏ(A1ââ¯âAk) for all A1,â¦,Ak, where ÏÏ(A) stands for the peripheral spectrum of A, if and only if Φ is an isomorphism or an anti-isomorphism multiplied by an mth root of unity, and the latter case occurs only if the generalized product is quasi-semi Jordan. If X1=H and X2=K are complex Hilbert spaces, we characterize also maps preserving the peripheral spectrum of the skew generalized products, and prove that such maps are of the form Aâ¦cUAUâ or Aâ¦cUAtUâ, where UâB(H,K) is a unitary operator, câ{1,â1}.
Journal: Linear Algebra and its Applications - Volume 468, 1 March 2015, Pages 87-106