Journal of Operator Theory
Volume 32, Issue 2, Fall 1994 pp. 353-379.
Continuity of the constant of hyperreflexivityAuthors: 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.
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