Geodesic
BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY
Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 145-154

Voir la notice de l'article provenant de la source Cambridge University Press

Let T be a bounded linear operator on a Banach space W, assume W and Y are in normed duality, and assume that T has adjoint T† relative to Y. In this paper, conditions are given that imply that for all λ≠0, λ−T and λ −T† maintain important standard operator relationships. For example, under the conditions given, λ −T has closed range if, and only if, λ −T† has closed range.These general results are shown to apply to certain classes of integral operators acting on spaces of continuous functions.
DOI : 10.1017/S0017089507003503
Mots-clés : 47A05 
BARNES, BRUCE A. BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY. Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 145-154. doi: 10.1017/S0017089507003503
@article{10_1017_S0017089507003503,
     author = {BARNES, BRUCE A.},
     title = {BOUNDED {LINEAR} {OPERATORS} {ON} {SPACES} {IN} {NORMED} {DUALITY}},
     journal = {Glasgow mathematical journal},
     pages = {145--154},
     year = {2007},
     volume = {49},
     number = {1},
     doi = {10.1017/S0017089507003503},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003503/}
}
TY  - JOUR
AU  - BARNES, BRUCE A.
TI  - BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY
JO  - Glasgow mathematical journal
PY  - 2007
SP  - 145
EP  - 154
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003503/
DO  - 10.1017/S0017089507003503
ID  - 10_1017_S0017089507003503
ER  - 
%0 Journal Article
%A BARNES, BRUCE A.
%T BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY
%J Glasgow mathematical journal
%D 2007
%P 145-154
%V 49
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003503/
%R 10.1017/S0017089507003503
%F 10_1017_S0017089507003503

[1] 1.Abramovich, Y. and Aliprantis, C., An invitation to operator theory, Graduate Studies in Math. no. 50 (Amer. Math. Soc., 2002). Google Scholar

[2] 2.Barnes, B., Fredholm theory in a Banach algebra of operators, Proc. Royal Irish Acad. 87A (1987), 1–11. Google Scholar

[3] 3.Barnes, B., Restrictions of bounded linear operators: closed range; Proc. Amer. Math. Soc., to appear. Google Scholar

[4] 4.Douglas, R., On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. Google Scholar

[5] 5.Folland, G., Real analysis, (John Wiley & Sons, 1984). Google Scholar

[6] 6.Folland, G., A course in abstract harmonic analysis (CRC Press, Boca Raton, 1995). Google Scholar

[7] 7.Jorgens, K., Linear integral operators (Pitman, Boston, 1982). Google Scholar

[8] 8.Lay, D. and Taylor, A., Introduction to functional analysis (2nd Edition), (Wiley, New York, 1980). Google Scholar

[9] 9.Kress, R., Linear integral equations, Applied Math. Sci. no. 82 (2nd Edition), (Springer, Verlag, 1989). Google Scholar

Cité par Sources :