HilbertC-模中融合框架的新定义及其系数的最小性-兰州大学.PDFVIP

兰州大学学报: 自然科学版, 2016, 52(2) / 4 月 Journal of Lanzhou University ：Natural Sciences，2016 ，52(2) / April ∗ Hilbert C -模中融合框架的新定义及其系数的 最小性 相中启, 李永明 上饶师范学院 数学与计算机科学学院, 江西, 上饶 334001 ∗ 摘 要：观察到Hilbert C -模中融合框架原定义的不合理性, 通过权重集的选取将其改进, 得到融合 ∗ 框架的新定义并给出了新定义的等价形式. 得到了Hilbert C -模中融合框架系数的一个最小性质, 作 为该性质的应用, 给出了融合框架去掉某个框架元素后不再成为融合框架的条件. ∗ 关键词：Hilbert C -模; 融合框架; 新定义; 等价定义; 最小性 中图分类号：O174.6 文献标识码：A 文章编号: 0455-2059(2016)02-0258-05 DOI: 10.13885/j.issn.0455-2059.2016.02.015 A new definition of fusion frames and the minimality of fusion ∗ frame coefficients in Hilbert C -modules Xiang Zhong-qi, Li Yong-ming College of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001, Jiangxi, China ∗ Abstract: An observation showed that the original definition of fusion frames in Hilbert C -modules was unrea- sonable and was improved by a replacement of the weight set, and a new definition of fusion frames was thus obtained. An equivalent form of the new definition of fusion frames was also given. A minimality property of fusion frame coefficients was obtained, and a condition for one fusion frame to be a non-frame set after the de- letion of one element from the fusion frame was given to illuminate the property. ∗ Key words: Hilbert C -module; fusion frame; new definition; equivalent definition; minimality AMS Subject Classifications (2000): 46L99; 42C15