论文标题
框架和基地的扩展-II
Extension of frames and bases -- II
论文作者
论文摘要
运算符值帧（$ g $ -frame），作为框架的概括，由Kaftal，Larson和Zhang引入\ textit {trans。阿米尔。数学。 soc。}，361（12）：6349-6385，2009 un \ textit {j。数学。肛门。 Appl。}，322（1）：437-452，2006。它在论文中进一步扩展了Arxiv：1810.01629 [Math.oa] 2018年10月3日，以便拥有有关Hilbert Space的操作员值的丰富理论，以及Banach Space。当索引集是一个测量空间时，在本文中已经研究了连续版本。我们研究此扩展的二元性，相似性，正交性和稳定性。给出了几种特征，包括当测量空间是局部紧凑的群体时的显着表征。当希尔伯特空间是有限的尺寸时，会得出变化公式，尺寸公式和痕量公式。
Operator-valued frame ($G$-frame), as a generalization of frame is introduced by Kaftal, Larson, and Zhang in \textit{Trans. Amer. Math. Soc.}, 361(12):6349-6385, 2009 and by Sun in \textit{J. Math. Anal. Appl.}, 322(1):437-452, 2006. It has been further extended in the paper arXiv:1810.01629 [math.OA] 3 October 2018, so as to have a rich theory on operator-valued frames for Hilbert spaces as well as for Banach spaces. The continuous version has been studied in this paper when the indexing set is a measure space. We study duality, similarity, orthogonality and stability of this extension. Several characterizations are given including a notable characterization when the measure space is a locally compact group. Variation formula, dimension formula and trace formula are derived when the Hilbert space is finite dimensional.
