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摘要
The standard commutants in a noncommutative algebra are derived from commutativity which in terms of Lie algebras means (adT)(n)(S) = 0. Some %26quot;weaker commutativities%26quot; given by vanishing (asymptotic vanishing) properties of the powers of adT, for instance (adT)(n)(S) = 0 or lim(n -%26gt;infinity) parallel to(adT)(n)(S)parallel to(1/n) = 0 when T and S are bounded linear operators on some complex Banach space, describe in a similar way different type of %26quot;weaker commutants%26quot;. This paper studies these %26quot;weaker commutants%26quot; and their corresponding compositions, in particular %26quot;weaker bicommutants%26quot;, in connection with J. von Neumann%26apos;s classical bicommutant theorem.
- 出版日期2014
