Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure
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In this paper, we show that every infinite dimensional Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure. Therefore, it resolves a long-standing question.
Keywordsmeasure of non-compactness inequivalence Banach space
MSC(2010)47H08 46B42 46B50 46B04
This work was supported by National Natural Science Foundation of China (Grant Nos. 11731010, 11471271 and 11471270). The authors thank the referees for their constructive comments, which suggest that besides the Hausdorff and Kuratowski measures of non-compactness, many other measures of non-compactness are also widely used in many aspects of nonlinear analysis. They also thank the teachers and students in Xiamen University Functional Analysis Seminar who made many helpful conversations on this paper.
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