On tractability and ideal problem in non-associative operator algebras
The paper centers around the following problem by \textit{W.\,Wojtyński} [Bull.\ Acad.\ Polon.\ Sci.\ 24, 797--801 (1976; Zbl 0356.47015)]: Does every closed Lie algebra of compact quasinilpotent operators on a Banach space contain a non-trivial closed Lie ideal? The authors give several partial answers and, approaching the problem from different directions, they find certain tools and introduce some concepts that might be of independent interest. One of the approaches is based on the concept of a tractable Lie algebra, which can be of interest independently of the main theme of the paper. Among other results, it is shown that an infinite-dimensional closed Lie or Jordan algebra of compact operators cannot be simple. Several partial answers to Wojtyński's problem on the topological simplicity of Lie algebras of compact quasinilpotent operators are also given.
scientific article; zbMATH DE number 5774015
scientific article