Projections in the convex hull of three isometries on absolutely continuous function spaces
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2021-04-26Abstract
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.
Palabra/s clave
Convex combination of isometries
Absolutely continuous function
Generalized bi-circular projection
Surjective linear isometry