In this paper, our central focus is upon a class of linear operators acting on a Banach space X called relatively pseudo weakly demicompact operators. We clarify and determine the relationships with pseudo upper semi-Fredholm and pseudo Fredholm operators. Moreover, a characterization by means of an axiomatic measure of weak noncompactness of linear operators is established. Our results are subsequently used to investigate the relationship between the essential pseudospectrum of the sum of two linear operators and the essential pseudospectrum of each of these operators.

中文翻译：

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相对 $$\varepsilon$$-伪弱半紧实度和弱非紧实度的度量

在本文中，我们的中心焦点是一类作用于 Banach 空间 X 的线性算子，称为相对伪弱半紧算算子。我们阐明并确定与伪上半 Fredholm 和伪 Fredholm 算子的关系。此外，建立了通过线性算子弱非紧性公理测度的表征。我们的结果随后用于研究两个线性算子之和的基本伪谱与这些算子中的每一个的基本伪谱之间的关系。