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On an Ideal in Algebras of Unbounded Operators
Author(s) -
Timmermann W.
Publication year - 1979
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.19790910127
Subject(s) - mathematics , ideal (ethics) , closure (psychology) , pure mathematics , set (abstract data type) , representation (politics) , space (punctuation) , algebra over a field , computer science , epistemology , politics , economics , political science , law , market economy , programming language , operating system , philosophy
The closure of the set of finite dimensional operators of ℒ + with respect to different topologies is considered. The obtained ideals have many properties similar to those of the ideal of completely continuous operators on H ILBERT space. For example, under some appropriate assumptions all continuous functionals are normal, irreducible representations are equivalent to the identical representation and so on.