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Operators whose ranges are contained in the null space of conditional expectations
Author(s) -
Jabbarzadeh M. R.,
Sharifi M. H.
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800066
Subject(s) - mathematics , conditional expectation , kernel (algebra) , type (biology) , algebra over a field , space (punctuation)
The goal of this article is to study the algebra D φ of a conditional type operators onL 2 ( Σ )such that each of members of D φ has its range contained in the kernel of a conditional expectation E . We present characterizations of this algebra in terms of (φ 0 ) 0 ‐type sub‐sigma algebras of Σ.