论文标题
关于任意序列的强烈部分贪婪基础
Strong Partially Greedy Bases with respect to An Arbitrary Sequence
论文作者
论文摘要
对于Schauder Bases，Dilworth等。引入并表征了部分贪婪的财产，该财产严格比（几乎）贪婪的财产要弱。后来，Berasategui等。定义并研究了一般基础的强大部分贪婪的特性。令$ \ mathbf n $成为积极整数的严格增加序列。在本文中，我们针对$ \ Mathbf n $定义了强大的部分贪婪的财产，称为（$ \ Mathbf n $，强烈的部分贪婪）。我们给出了这一新属性的特征，即（$ \ Mathbf n $，强烈的部分贪婪）属性$ \ mathbf n $，确定lebesgue-type不平等的不平等现象（$ \ mathbf n $（$ \ mathbf n $）（$ \ mathbf n $，强烈的部分贪婪）参数，调查（调查）部分贪婪），仅举几例。此外，我们介绍了（$ \ mathbf n $，几乎是贪婪）的财产，并将该属性等同于加强（$ \ Mathbf n $，强烈的部分贪婪）财产。可以将本文视为对强烈部分贪婪基础的最新结果的调查，也可以将这些结果扩展到任意序列而不是$ \ Mathbb {n} $。
For Schauder bases, Dilworth et al. introduced and characterized the partially greedy property, which is strictly weaker than the (almost) greedy property. Later, Berasategui et al. defined and studied the strong partially greedy property for general bases. Let $\mathbf n$ be any strictly increasing sequence of positive integers. In this paper, we define the strong partially greedy property with respect to $\mathbf n$, called the ($\mathbf n$, strong partially greedy) property. We give characterizations of this new property, study relations among ($\mathbf n$, strong partially greedy) properties for different sequences $\mathbf n$, establish Lebesgue-type inequalities for the ($\mathbf n$, strong partially greedy) parameter, investigate ($\mathbf n$, strong partially greedy) bases with gaps, and weighted ($\mathbf n$, strong partially greedy) bases, to name a few. Furthermore, we introduce the ($\mathbf n$, almost greedy) property and equate the property to a strengthening of the ($\mathbf n$, strong partially greedy) property. This paper can be viewed both as a survey of recent results regarding strong partially greedy bases and as an extension of these results to an arbitrary sequence instead of $\mathbb{N}$.
