Hilbert C*-模中融合框架的新定义及其系数的最小性

A new definition of fusion frames and the minimality of fusion frame coefficients in Hilbert C*-modules

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.

An observation showed that the original definition of fusion frames in Hilbert C＊-modules was unreasonable 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 deletion of one element from the fusion frame was given to illuminate the property.