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On the bounded closure of the range of an operator
Author(s):
Robin
Harte;
Woo
Young
Lee
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2313-2318.
MSC (1991):
Primary 47A05;
Secondary 47B07, 46B06
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Abstract:
The ``bounded closure of the range" of an operator between two normed spaces is a linear subspace lying between the range and its closure. The induced concept of ``almost onto" is a sort of first draft of the concept of ``almost open".
References:
- 1.
- E. Albrecht and R. D. Mehta, Some remarks on local spectral theory, Jour. Operator Theory 2 (1984), 285-317. MR 85m:47031
- 2.
- J. J. Buoni, R. E. Harte and A. W. Wickstead, Upper and lower Fredholm spectra, Proc. Amer. Math. Soc. 66 (1977), 309-314. MR 56:12925
- 3.
- S. R. Caradus, W. E. Pfaffenberger and B. Yood, Calkin algebras and algebras of operators on Banach spaces, (Dekker New York 1974). MR 54:3434
- 4.
- J. Dieudonne, Foundations of Modern Analysis, (Academic Press 1960). MR 22:11074
- 5.
- R. E. Harte, Almost open mappings between normed spaces, Proc. Amer. Math. Soc. 90 (1984), 243-249. MR 85b:47024
- 6.
- R. E. Harte, Invertibility and singularity, (Dekker New York 1988). MR 89d:47001
- 7.
- R. E. Harte and M. Mathieu, Enlargements of almost open mappings, Proc. Amer. Math. Soc. 96 (1986), 247-248. MR 87e:47002
- 8.
- R. E. Harte and G. P. Shannon, On closed subspaces of operator ranges, Proc. Amer. Math. Soc. 118 (1993), 171-173. MR 93f:47001
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Additional Information:
Robin
Harte
Affiliation:
School of Mathematics, Trinity College, Dublin, Ireland
Email:
rharte@maths.tcd.ie
Woo
Young
Lee
Affiliation:
Department of Mathematics, Sung Kwan University, Suwon 440-746, Korea
Email:
wylee@yurim.skku.ac.kr
DOI:
10.1090/S0002-9939-97-03803-3
PII:
S 0002-9939(97)03803-3
Keywords:
Bounded closure,
almost onto,
almost open
Received by editor(s):
August 22, 1995
Received by editor(s) in revised form:
February 1, 1996
Additional Notes:
The second author was supported by KOSEF grants 941-0100-028-2 and 94-0701-02-01-3.
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1997,
American Mathematical Society
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