On the Symmetrizations of -Isometries on Positive Cones of Continuous Function Spaces

Let be a compact Hausdorff space, be the real Banach space of all continuous functions on endowed with the supremum norm, and be the positive cone of . A weak stability result for the symmetrization of a general -isometry from to a Banach space is obtained: For any element , there exists a such that...

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Bibliographic Details
Published in:Functional analysis and its applications 2021, Vol.55 (1), p.75-79
Main Author: Sun, Longfa
Format: Article
Language:English
Subjects:
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639/766/189
639/766/530
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Analysis
Banach spaces
Cones
Continuity (mathematics)
Function space
Functional Analysis
Mathematics
Mathematics and Statistics
Stability
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Summary:Let be a compact Hausdorff space, be the real Banach space of all continuous functions on endowed with the supremum norm, and be the positive cone of . A weak stability result for the symmetrization of a general -isometry from to a Banach space is obtained: For any element , there exists a such that This result is used to prove new stability theorems for the symmetrization of .
ISSN:0016-2663
1573-8485
DOI:10.1134/S0016266321010081