The ascent and descent of weighted conditional expectation operators

Yousef Estaremi

paper

The ascent and descent of weighted conditional expectation operators

arXiv:1711.01540

Abstract

In this paper we prove that the ascent of a weighted conditional expectation operator of the form of $M_{w} E M_{u}$ on $L^{p}$ -spaces is always finite and is equal to 2. Also we get that under a weak condition the descent of $M_{w} E M_{u}$ is finite and is equal to 2 too. Moreover, we give some necessary and sufficient conditions for $M_{w} E M_{u}$ to be power bounded. In the sequel we apply some results in operator theory on ascent and descent to $M_{w} E M_{u}$ . Finally we find that $T = M_{w} E M_{u}$ is Cesaro bounded if and only if $T$ is Cesaro bounded.

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