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Approximate orthogonality in normed spaces and its applications II
Linear Algebra and its Applications ( IF 1.1 ) Pub Date : 2021-09-14 , DOI: 10.1016/j.laa.2021.09.011
Paweł Wójcik 1
Affiliation  

In a normed space we consider an approximate orthogonality relation related to the Birkhoff orthogonality B. We prove thatxBεyzLin{x,y}xBz,zyεyφJ(x)|φ(y)|εy. Such a characterization was already proved in [Linear Algebra Appl. 531 (2017), 305–317] for real normed spaces. This result is a useful theoretical tool that was used in many papers. Therefore, we prove it now for complex normed spaces, as well as give some new applications. In particular, we extend the Arambašić-Rajić Theorem. Moreover, this paper presents some result concerning the problem of minimal extensions of continuous linear operators from hyperplanes; namely, some estimation for λA(Y,X) is proved.



中文翻译:

赋范空间中的近似正交性及其应用 II

在赋范空间中,我们考虑与 Birkhoff 正交性相关的近似正交性关系 . 我们证明Xεz{X,}Xz,z-εφJ(X)|φ()|ε.这种表征已经在[线性代数应用程序。531 (2017), 305–317] 用于实赋范空间。该结果是许多论文中使用的有用理论工具。因此,我们现在针对复杂的赋范空间证明它,并给出一些新的应用。特别是,我们扩展了 Arambašić-Rajić 定理。此外,本文还提出了关于连续线性算子从超平面的最小扩展问题的一些结果;即,一些估计λ一种(,X) 被证明。

更新日期:2021-09-15
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