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International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 565-570
http://dx.doi.org/10.1155/S0161171298000787

Some properties of prereflexive subspaces of operators

Department of Mathematics, University of Science and Technology of China, Hefei,, Anhui 230026, China

Received 31 May 1995; Revised 10 December 1995

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the paper, we define a notion of prereflexivity for subspaces, give several equivalent conditions of this notion and prove that if SL(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 A0 is not prereflexive.