Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js
Previous issue ·  Next issue ·  Most recent issue in the archive · All issues in the archive   

Journal of Operator Theory

Volume 32, Issue 2, Fall 1994  pp. 353-379.

Continuity of the constant of hyperreflexivity

Authors: Ileana IonaÅŸcu
Author institution:Pure Mathematics Department, University of Waterloo, Waterloo, Ontario, N2L 3G1, CANADA and The Fields Institute, 180 Columbia St. West, Waterloo, Ontario N2L 5Z5, CANADA. On leave from: The Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, ROMANIA

Summary: Starting from the question of what are the possible values of the constant of hyperreflexivity for subspaces of B(H), where H is a separable complex Hilbert space, the paper considers the continuity of the function κ:B(H)ˉR, defined by κ(T)=K(Aw(T)),Aw(T))denotingtheunitalweaklyclosedalgebrageneratedbyT.Asaconsequence,itisshownthatanynumberbiggerthanorequaltooneisaconstantofhyperreflexivityofasubspace.Besidesseveralresultsconcerningthecontinuityofthefunction\kappa$, the paper contains also more general results, like those determining the closures (in the norm topology) or the set of reflexive, respectively non-reflexive, operators.

Keywords: Hyperreflexivity, invariant subspace, Hilbert space.


Contents    Full-Text PDF