The ascent and descent of weighted conditional expectation operators

2017/11/05 by Yousef Estaremi, Estaremi, Yousef
Computer Science · Decision Sciences · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Functional Analysis (math.FA) #Multi-Criteria Decision Making #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1711.01540

openalex publication_date 2017/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that the ascent of a weighted conditional expectation operator of the form of M_wEM_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_wEM_u is finite and is equal to 2 too. Moreover, we give some necessary and sufficient conditions for M_wE M_u to be power bounded. In the sequel we apply some results in operator theory on ascent and descent to M_wEM_u. Finally we find that T=M_wEM_u is Cesaro bounded if and only if \widehatT is Cesaro bounded.

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