Generalized probabilistic approximation characteristic based on Birkhoff orthogonality and related conclusions in $S_{\infty}$-norm

Weiye Zhang; Chong Wang; Huan Li

doi:10.33205/cma.1807082

Generalized probabilistic approximation characteristic based on Birkhoff orthogonality and related conclusions in $S_{\infty}$-norm

Abstract

In this article, we generalize the definition of the probabilistic Gel'fand width from the Hilbert space to the strictly convex reflexive space by giving Birkhoff left orthogonal decomposition theorem. Meanwhile, a more natural definition of Gel'fand width in the classical setting is selected to make sure probabilistic and average Gel'fand widths will not lose their meaning, so that we can give the equality relation between the probabilistic Gel'fand width and the probabilistic linear width of the Hilbert space. Meanwhile, we use this relationship to continue the study of the Gel'fand widths of the univariate Sobolev space and the multivariate Sobolev space, especially in $S_{\infty}$-norm, and determine the exact order of probabilistic and average Gel'fand widths.

Keywords

References

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Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis, Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Weiye Zhang
0009-0007-3318-5098
China

Chong Wang
0009-0005-5380-0217
China

Huan Li ^*
0009-0000-8943-2907
China

Early Pub Date

December 12, 2025

Publication Date

December 15, 2025

Submission Date

October 20, 2025

Acceptance Date

December 5, 2025

Published in Issue

Year 2025 Volume: 8 Number: 4

DOI

https://doi.org/10.33205/cma.1807082

IZ

https://izlik.org/JA62HL56WE

Cite

RIS / Bibtex

APA

Zhang, W., Wang, C., & Li, H. (2025). Generalized probabilistic approximation characteristic based on Birkhoff orthogonality and related conclusions in $S_{\infty}$-norm. Constructive Mathematical Analysis, 8(4), 228-240. https://doi.org/10.33205/cma.1807082

AMA

1.Zhang W, Wang C, Li H. Generalized probabilistic approximation characteristic based on Birkhoff orthogonality and related conclusions in $S_{\infty}$-norm. CMA. 2025;8(4):228-240. doi:10.33205/cma.1807082

Chicago

Zhang, Weiye, Chong Wang, and Huan Li. 2025. “Generalized Probabilistic Approximation Characteristic Based on Birkhoff Orthogonality and Related Conclusions in $S_{\infty}$-Norm”. Constructive Mathematical Analysis 8 (4): 228-40. https://doi.org/10.33205/cma.1807082.

EndNote

Zhang W, Wang C, Li H (December 1, 2025) Generalized probabilistic approximation characteristic based on Birkhoff orthogonality and related conclusions in $S_{\infty}$-norm. Constructive Mathematical Analysis 8 4 228–240.

IEEE

[1]W. Zhang, C. Wang, and H. Li, “Generalized probabilistic approximation characteristic based on Birkhoff orthogonality and related conclusions in $S_{\infty}$-norm”, CMA, vol. 8, no. 4, pp. 228–240, Dec. 2025, doi: 10.33205/cma.1807082.

ISNAD

Zhang, Weiye - Wang, Chong - Li, Huan. “Generalized Probabilistic Approximation Characteristic Based on Birkhoff Orthogonality and Related Conclusions in $S_{\infty}$-Norm”. Constructive Mathematical Analysis 8/4 (December 1, 2025): 228-240. https://doi.org/10.33205/cma.1807082.

JAMA

1.Zhang W, Wang C, Li H. Generalized probabilistic approximation characteristic based on Birkhoff orthogonality and related conclusions in $S_{\infty}$-norm. CMA. 2025;8:228–240.

MLA

Zhang, Weiye, et al. “Generalized Probabilistic Approximation Characteristic Based on Birkhoff Orthogonality and Related Conclusions in $S_{\infty}$-Norm”. Constructive Mathematical Analysis, vol. 8, no. 4, Dec. 2025, pp. 228-40, doi:10.33205/cma.1807082.

Vancouver

1.Weiye Zhang, Chong Wang, Huan Li. Generalized probabilistic approximation characteristic based on Birkhoff orthogonality and related conclusions in $S_{\infty}$-norm. CMA. 2025 Dec. 1;8(4):228-40. doi:10.33205/cma.1807082