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.
[1, Theorem 4.4] states that every infinite dimensional Banach space admits a homogenous measure of noncompactness not equivalent to the Hausdorff measure. Howevere, there is a gap in the proof. In fact,we found that ...[1, Theorem 4.4] states that every infinite dimensional Banach space admits a homogenous measure of noncompactness not equivalent to the Hausdorff measure. Howevere, there is a gap in the proof. In fact,we found that [1, Lemma 4.3] is not true. In this erratum, we give a corrected proof of [1, Theorem 4.4].展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11731010,11471271 and 11471270)
文摘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.
基金supported by National Natural Science Foundation of China(Grant No.11731010)
文摘[1, Theorem 4.4] states that every infinite dimensional Banach space admits a homogenous measure of noncompactness not equivalent to the Hausdorff measure. Howevere, there is a gap in the proof. In fact,we found that [1, Lemma 4.3] is not true. In this erratum, we give a corrected proof of [1, Theorem 4.4].
