International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 565-570
doi:10.1155/S0161171298000787
Some properties of prereflexive subspaces of operators
Jiankui Li
Department of Mathematics, University of Science and Technology of China, Hefei,, Anhui 230026, China
Abstract
In the paper, we define a notion of prereflexivity for subspaces, give several equivalent conditions of this notion and prove that if S⫅L(H) is prereflexive, then every σ-weakly closed subspace of S is prereflexive if and only if S has the property WP(see definition 2.11). By our result, we construct a reflexive operator A such that A⊕0 is not prereflexive.