Subspace maps of operators on Hilbert space
Author:
W. E. Longstaff
Journal:
Proc. Amer. Math. Soc. 84 (1982), 195201
MSC:
Primary 47A05; Secondary 47A10
MathSciNet review:
637168
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: An operator acting on a Hilbert space gives rise to a map on the set of subspaces of given by , where denotes norm closure. This map is called the subspace map of . By identifying subspaces with projections in the usual way it is shown that for , is uniformly (respectively, strongly) continuous if and only if the approximate point spectrum of does not contain 0. In this case it is proved that preserves the property of being uniformly (respectively, strongly, weakly) closed and its effect on reflexivity is described.
 [1]
H.J. Bandelt, Tight residuated mappings and extensions, (Proc. Colloq. on Universal Algebra, Esztergom, 1977), Colloq. Math. Soc. János Bolyai; Universal Algebra.
 [2]
Sterling
K. Berberian, Lectures in functional analysis and operator
theory, SpringerVerlag, New YorkHeidelberg, 1974. Graduate Texts in
Mathematics, No. 15. MR 0417727
(54 #5775)
 [3]
R.
G. Douglas and Carl
Pearcy, On a topology for invariant subspaces, J. Functional
Analysis 2 (1968), 323–341. MR 0233224
(38 #1547)
 [4]
P.
R. Halmos, Reflexive lattices of subspaces, J. London Math.
Soc. (2) 4 (1971), 257–263. MR 0288612
(44 #5808)
 [5]
W.
E. Longstaff, A note on transforms of subspaces of
Hilbert space, Proc. Amer. Math. Soc.
76 (1979), no. 2,
268–270. MR
537086 (80i:47054), http://dx.doi.org/10.1090/S00029939197905370869
 [1]
 H.J. Bandelt, Tight residuated mappings and extensions, (Proc. Colloq. on Universal Algebra, Esztergom, 1977), Colloq. Math. Soc. János Bolyai; Universal Algebra.
 [2]
 S. K. Berberian, Lectures in functional analysis and operator theory, SpringerVerlag, Berlin and New York, 1974. MR 0417727 (54:5775)
 [3]
 R. G. Douglas and Carl Pearcy, On a topology for invariant subspaces, J. Funct. Anal. 2 (1968), 323341. MR 0233224 (38:1547)
 [4]
 P. R. Halmos, Reflexive lattices of subspaces, J. London Math. Soc. 4 (1971), 257263. MR 0288612 (44:5808)
 [5]
 W. E. Longstaff, A note on transforms of subspaces of Hilbert space, Proc. Amer. Math. Soc. 76 (1979), 268270. MR 537086 (80i:47054)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC:
47A05,
47A10
Retrieve articles in all journals
with MSC:
47A05,
47A10
Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198206371687
PII:
S 00029939(1982)06371687
Article copyright:
© Copyright 1982
American Mathematical Society
