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The Range Sequence of an Operator

Published online by Cambridge University Press:  20 November 2018

F.-H. Vasilescu
F.-H. Vasilescu*
Affiliation:
Institute of Mathematics, Bucharest, Rumania
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Let T be a linear operator on a Banach space X and consider the sequence of ranges

where the inclusions are not necessarily proper. The linear subspaces Xn=TnX (n>0) are, in general, not closed but they have some remarkable properties [1], [2]. Let X0=X and denote by |x|0 (x∈X0) the norm of X0.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 145 - 147
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Fillmore, P. A. and Williams, J. P., On operator ranges, (preprint), Advances in Math. 7 (1971), 254-281.Google Scholar
2. Foias, C., Invariant para-closed subspaces, Indiana Univ. Math. J. 20 (1971), 897-900.Google Scholar
3. Grabiner, S., Ranges of quasinilpotent operators, Illinois J. Math. 15(1971), 150-152.Google Scholar