نگهدارنده های جمعی وارون دریزین روی فضای $B_s(H)$

Document Type : Research Paper

Authors

گروه ریاضی کاربردی، دانشگاه تحصیلات تکمیلی صنعتی و فناوری پیشرفته، کرمان ، ایران

10.22072/wala.2021.533966.1334

Abstract

فرض کنید $B_s(H)$ جبر جردن همه عملگرهای خودالحاق کراندار روی فضای جدایی پذیر هیلبرت $H$ باشد. در این مقاله به بررسی همه نگاشت های جمعی و دوسویی $\phi:B_s(H)\longrightarrow B_s(H)$ که وارون دریزین عملگرها(درصورت وجود) را حفظ می نمایند، می پردازیم. نتیجه اصلی این مقاله به این شکل است که اگر برای هر عملگر تصویر $P$ روابط $\phi(\mathbb{R}P)\subset \mathbb{R}\phi(P)$ و $\phi(PB_s(H)P)= \phi(P)B_s(H)\phi(P)$ برقرار باشند، آنگاه عملگر یکانی یا پادیکانی $U:H\rightarrow H$
وجود دارد به طوری که $\phi(T)=UTU^*$، برای هر $T\in B_s(H)$.

Keywords


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