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On further properties of improjective operators

Published online by Cambridge University Press:  09 April 2009

E. Tarafdar
E. Tarafdar
Affiliation:
School of Mathematical Sciences Flinders UniversitySouth Australia
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This is a continuation of our work [4]. The purpose of this paper is to find the relation of the class of improjective operators on some Banach space, with the classes of strictly singular, strictly cosingular and φ-admissible perturbations on X and to investigate those pairs of Banach spaces for which all bounded linear operators having either of the pair as domain and the other as range are improjective, or strictly singular. The beginning of Section 1 is intended to familiarize the reader with the concepts and notations used in this paper.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 3 , November 1972 , pp. 352 - 363
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Kato, T., ‘Perturbation theory, nullity, deficiency and other quantities of linear operators’, J. Analyse Math. 6 (1958), 261–322.Google Scholar
[2]Goldberg, S., Unbounded linear operators, Theory and applications, (McGraw-Hill (1966).Google Scholar
[3]Pelczynski, A., ‘On strictly singular and strictly consingular operators I and II’, Bull. Acad. Polon. Sci. 13 (1965), 31–41.Google Scholar
[4]Tarafdar, E., ‘Improjective operators and ideals in a category of Banach spaces’, J. Austral. Math. Soc. 14 (1972), 274–292.Google Scholar
[5]Cohberg, I. C., Markus, A. S. and Feldman, I. A., ‘Normally soluble operators and ideals associated with them Iav. Moldavask.’ (Russian). Fil. Akad. Nauk SSSR 10, no. 76 (1960), 51–59.Google Scholar
[6]Dunford, N. and Schwartz, J., Linear operators I: General theory, Pure and Applied Math. vol. 7, (Interscience, New York, (1958).)Google Scholar
[7]Pfaffenberger, W., ‘On the ideals of strictly singular and inessential operators,’ Proc. Amer. Math. Soc. 25 (1970), 603–607.CrossRefGoogle Scholar
[8]Kleinecke, D., ‘Almost-finite, compact, and inessential operators’, Proc. Amer. Math. Soc. 14 (1963), 863–868.Google Scholar
[9]Schechter, M., ‘Riesz operators and Fredholm perturbations’, Bull. Amer. Math. Soc. 74 (1968) 1139–1144.Google Scholar
[10]Ju., N. Vladimirskii, ‘Strictly consingular operators’, Soviet Math. Dokl. vol. 8 no. 3 (1967), 739–740.Google Scholar
[11]Whitley, R. J., ‘Strictly singular operators and their conjugates’, Trans. Amer. Math. Soc. 113 (1964), 252–261.CrossRefGoogle Scholar
[12]Milman, V. D., ‘Certain properties of strictly singular operators’ (Russian) Funkeional Anal. i pritozen 3, no. 1 (1969), 93–94 MR 39 7 3332.Google Scholar
[13]Caradus, S. R., ‘Operators of Riesz type’, Pacific J. Math. 18 (1966), 61–71.CrossRefGoogle Scholar
[14]Pelczynski, A., ‘Projections in certain Banach spaces’, Studia Math. 19 (1960), 209–228.CrossRefGoogle Scholar
[15]Lindesntrauss, J., ‘On complemented subspaces of m’, Israel J. Math. 5 (1967), 153–156.CrossRefGoogle Scholar
[16]Goodner, D. B., ‘Projections in normed linear spaces’, Trans. Amer. Math. Soc. 69 (1950), 89–108.CrossRefGoogle Scholar
[17]Grothendieek, A., ‘Sur les applications linéaires faiblement compacts d'espaces du type C(K)’, Canad. J. Math. 5 (1953), 129–173.CrossRefGoogle Scholar
[18]Lacey, H. E. and Morris, P. D., ‘Continuous linear operators on spaces of continuous functions,’ Proc. Amer. Math. Soc. 17 (1966), 848–853.Google Scholar
[19]Day, M., Normed linear spaces (Springer, Berlin (1958)).CrossRefGoogle Scholar
[20]Kadec, M. and Pelczynski, A., ‘Bases, lacunary sequences and complemented subspaces in the spaces Lp,’ Studia Math. 21 (1962), 161–176.CrossRefGoogle Scholar
[21]Banach, S., Opérations linéaires (Chelsea, New York (1955)).Google Scholar