engleski

When the average of composition operators being a projection

The notion of a generalized bicircular projection on a Banach space is a counterpart of the notion of an orthogonal projection on a Hilbert space. It is known that every generalized bicircular projection on C_0(X), where X is a locally compact Hausdorff space, can be written as the average of the identity and a certain weighted composition operator. In this paper, we study the question of when the average of composition operators (resp. the convex combination of the identity and a composition operator) on C_0(X) is a projection. We also study the question of when the average (resp. the convex combination) of bounded linear operators on a general Banach space is a tripotent.

Generalized bicircular projections ; average of composition operators ; composition operators of continuous functions

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