Characterizations for a frame and its duals are known for separable Hilbert spaces. In this paper, we characterize a class of approximate Schauder frame and its duals for separable Banach spaces. We also give an operator-theoretic characterization for similarity of ASFs. Our results encode the results of Holub, Li, Balan, Han, and Larson. We also address orthogonality of ASFs.

中文翻译：

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对Banach空间的近似Schauder框架及其对偶的刻画

框架及其对偶的特征以可分离的希尔伯特空间而闻名。在本文中，我们刻画了一类用于可分离Banach空间的近似Schauder框架及其对偶。我们还给出了ASF相似性的算子理论表征。我们的结果编码了Holub，Li，Balan，Han和Larson的结果。我们还讨论了ASF的正交性。