论文标题
连续$ k $ - $ g $ -frames in Hilbert $ c^*$ - 模块
Continuous $K$-$g$-frames in Hilbert $C^*$-modules
论文作者
论文摘要
这项研究旨在将$ g $ -frame的概念和$ k $ -frame组合为Hilbert $ C^*$ - 模块$ U $，对于运营商$ k \ in End^*_ a（u）$，其中$ end^*_ a（u）$包含$ u $ $ u $的所有可搭接的$ a $ a $ a $ a $ linear maps。结果，引入和研究了Hilbert $ C^*$的连续$ K $ - $ G $ -FRAMES。随后，证明了连续$ k $ - $ g $ -f $ frames in Hilbert $ c^*$ - 模块的一些特征。接下来，引入了$ k $ - $ g $ - $ c $ - $ k $ - $ g $ -frame。最后，有些结果，尤其是连续$ k $ - $ g $ - $ dual的存在。
This study aims at combining the concepts of $g$-frame and $K$-frame for a Hilbert $C^*$-module $U$, for an operator $K \in End^*_A(U)$, where $End^*_A(U)$ contains all adjointable $A$-linear maps on $U$. As a result, continuous $K$-$g$-frames for Hilbert $C^*$-modules are introduced and studied. Subsequently, some characterizations of continuous $K$-$g$-frames in Hilbert $C^*$-modules are proved. Next, continuous $K$-$g$-dual of a $c$-$K$-$g$-frame is introduced. Finally, some results, particularly, the existence of continuous $K$-$g$-dual, are derived.
