弱Lorentz-Schatten空间中嵌入映射的熵数的估计
Estimation of the Entropy Numbersof Embedding between WeakLorentz-Schatten Spaces
摘要: 本文在有限维的情形下给出了弱Lorentz-Schatten空间中自然嵌入映射的熵数的估计，这可以看成是弱Lorentz序列空间中关于自然嵌入映射熵数估计的一种推广。
Abstract: In this paper, in the finite-dimensional case, the estimation of the entropy numbers ofthe embedding between the weak Lorentz-Schatten spaces is presented, which can beregarded as a generalization of the estimation of the entropy numbers of the embeddingbetween the weak lorentz sequence spaces.
文章引用：马宁, 韩亚洲, 赵兴鹏. 弱Lorentz-Schatten空间中嵌入映射的熵数的估计[J]. 应用数学进展, 2025, 14(6): 398-405. https://doi.org/10.12677/AAM.2025.146329

参考文献

[1] Pietsch, A.(1980)Operator Ideals. North-Holland Publishing, 1-365.
[2] Pajor, A.(1998) Metric Entropy of the Grassmann Manifold. In: Conver Geometric Analysis. Cambridge University Press, 181-188.
[3] Rohde, A. and Tsvbakov,A.B.(2011)Estimation of High-Dimensional Low-Rank Matrices.The Annals of Statistics, 39,887-930.
https://doi.org/10.1214/10-aos860
[4] Hinrichs, A., Prochno, J. and Vybíral, J. (2017) Entropy Numbers of Embeddings of SchattenClasses. Journal of Functional Analysis, 273,3241-3261.
[5] Dolezalová, A. and Vybíral, J. (2020)On the Volume of Unit Balls of Finite-DimensionalLorentz Spaces. Journal ofApprorimation Theory, 255, Article 105407.
https://doi.org/10.1016/j.jat.2020.105407
[6] Pisier, G. and Xu,Q.(2003)Non-Commutative Lp-Spaces. In: Handbook of the Geometry ofBanach Spaces, Elsevier, 1459-1517.
https://doi.org/10.1016/s1874-5849(03)80041-4
[7] Konig, H. (1986) Eigenvalue Distribution of Compact Operators, Volume 16 of Operator The-ory:Advances and Applications. Basel.
[8] Kossaczka, M. and Vybiral, J.(2020)Entropy Numbers of Finite-Dimensional Embed-dings.Erpositiones Mathematicae, 38,319-336.
[9] Edmunds, D.E. and Tiebel, H. (1996). Function Spaces, Entropy Numbers, Differential Operators. Cambridge University Press, 1-390.
https://doi.org/10.1017/cbo9780511662201
[10] Arazy, J. (1978) Some Remarks on Interpolation Theorems and the Boundness of the Triangu-lar Projection in Unitary Matrix Spaces.Integral Equations and Operator Theory, 1, 453-495.
[11] Bergh, J. and Lofstrom, J. (2012)Interpolation Spaces: An Introduction. Springer, 1-207
[12] Prochno, J., Sonnleitner, M. and Vybíral, J. (2025) Entropy Numbers of Finite-DimensionalLorentz Space Embeddings. Studia Mathematica, 255, Article 105407.
https://doi.org/10.4064/sm240409-15-2
[13] Schiitt, C.(1982)On the Volume of Unit Balls in Banach Spaces. Compositio Mathematica.47.393-407.
[14] Hinrichs, A., Kolleck, A. and Vybíral, J.(2016) Carl's Inequality for Quasi-Banach Spaces. Journal of Functional Analysis,271.2293-2307.

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