{"title":"连续$G$-框架的和与稳定性","authors":"Azam Yousefzadeheyni, M. R. Abdollahpour","doi":"10.22130/SCMA.2018.90101.472","DOIUrl":null,"url":null,"abstract":"In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"6 1","pages":"157-169"},"PeriodicalIF":0.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Sum and Stability of Continuous $G$-Frames\",\"authors\":\"Azam Yousefzadeheyni, M. R. Abdollahpour\",\"doi\":\"10.22130/SCMA.2018.90101.472\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.\",\"PeriodicalId\":38924,\"journal\":{\"name\":\"Communications in Mathematical Analysis\",\"volume\":\"6 1\",\"pages\":\"157-169\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22130/SCMA.2018.90101.472\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22130/SCMA.2018.90101.472","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
本文给出了连续$g$-系的有限和再次为连续$g$-系的若干条件。我们给出了连续的$g$-帧$Lambda=left{Lambda_w in blleft (H,K_wright): win Omegaright}$和$Gamma=left{Gamma_w in blleft (H,K_wright): win Omegaright}$以及$H$上的算子$U$和$V$的充分必要条件,使得$Lambda U+Gamma V={Lambda_w U+Gamma_w V in blleft (H,K_wright): win Omega}$又是一个连续的$g$-帧。此外,我们还得到了连续$g$-框架有限和在小扰动下稳定的几个充分条件。
In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.