Projections in the Convex Hull of Three Isometries on Absolutely Continuous Function Spaces

In this paper, we prove that any projection in the convex hull of three surjective linear isometries on AC ( X ) is a generalized bi-circular projection, where AC ( X ) denotes the Banach space of all absolutely continuous functions on a compact subset of R with at least two points. We also show tha...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2021, Vol.44 (5), p.3489-3509
Main Authors: Hosseini, Maliheh, Jiménez-Vargas, A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Banach spaces
Continuity (mathematics)
Convexity
Function space
Mathematics
Mathematics and Statistics
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Summary:In this paper, we prove that any projection in the convex hull of three surjective linear isometries on AC ( X ) is a generalized bi-circular projection, where AC ( X ) denotes the Banach space of all absolutely continuous functions on a compact subset of R with at least two points. We also show that the trivial projections are the only projections on AC ( X ) which can be represented as the average of three surjective linear isometries.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-021-01128-5