论文标题
公制，Schauder和操作员可价值框架
Metric, Schauder and Operator-Valued Frames
论文作者
论文摘要
已经引入了公制空间的框架和贝塞尔序列的概念。这个概念与Lipschitz的免费Banach空间有关。 \证明，每个可分开的度量空间都允许度量$ \ Mathcal {M} _D $ -FRAME。通过不含Lipschitz的Banach空间，表明公制空间的框架和Banach空间子集的框架之间存在对应关系。获得了公制框架的几个特征。还提出了稳定结果。引入和研究了非线性乘数。这个概念与Lipschitz紧凑型操作员的概念有关。讨论了乘数的连续性属性。 对于Banach空间的近似Schauder框架的子类，使用标准序列空间的标准Schauder基础得出表征结果。完全描述了近似Schauder框架子类的双重类。该类的相似性是特征的，并使用正交性得出插值结果。获得扩张结果。对于接受同质半米产品的Banach空间而得出了新的身份。该课程获得了一些稳定结果。 引入了希尔伯特空间的操作员值帧的概括，该框架统一了所有已知的希尔伯特空间框架概括。通过施加框架操作员的分解属性，对该概念进行了深入研究。它的二元性，相似性和正交性得到解决。该概念与群体和类似组的统一系统之间的联系。该课程的佩奇定理是得出的。
Notion of frames and Bessel sequences for metric spaces have been introduced. This notion is related with the notion of Lipschitz free Banach spaces. \ It is proved that every separable metric space admits a metric $\mathcal{M}_d$-frame. Through Lipschitz-free Banach spaces it is showed that there is a correspondence between frames for metric spaces and frames for subsets of Banach spaces. Several characterizations of metric frames are obtained. Stability results are also presented. Non linear multipliers are introduced and studied. This notion is connected with the notion of Lipschitz compact operators. Continuity properties of multipliers are discussed. For a subclass of approximated Schauder frames for Banach spaces, characterization result is derived using standard Schauder basis for standard sequence spaces. Duals of a subclass of approximate Schauder frames are completely described. Similarity of this class is characterized and interpolation result is derived using orthogonality. A dilation result is obtained. A new identity is derived for Banach spaces which admit a homogeneous semi-inner product. Some stability results are obtained for this class. A generalization of operator-valued frames for Hilbert spaces are introduced which unifies all the known generalizations of frames for Hilbert spaces. This notion has been studied in depth by imposing factorization property of the frame operator. Its duality, similarity and orthogonality are addressed. Connections between this notion and unitary representations of groups and group-like unitary systems are derived. Paley-Wiener theorem for this class are derived.
