k-框架是框架的一种推广.本文在HIlbErT空间将紧框架推广到k-框架上,引入紧k-框架的概念.通过紧k-框架的算子k和合成算子给出紧k-框架的算子刻画,并利用紧k-框架的算子k给出紧k-框架成为紧框架的一个充要条件.还讨论紧k-框架的构造以及两个紧k-框架集的包含与涉及的算子k的相互关系.K-frames are the generalizations of frames.In this paper,we introduce the definition of a tight K-frame in a Hilbert space,then we give a characterization for tight K-frames by the synthesis operator and the operator K.By means of the operator K,we also obtain a necessary and sufficient condition for tight K-frames to be tight frames.In the end we make a discussion on the construction for tight K-frame and the correlations between two tight K-frames and the involved operator K.国家自然科学基金(61170324); 天元基金(11226099); 福建省自然科学基金(2012J01005); 福建省教育厅资助科技项目(JA11100); 福州大学科研启动项目(022410); 福州大学科技发展基金项目(2012-XQ-29
