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On interpolation of strictly (co-)singular linear operators

  • O. J. Beucher (a1)

We show that the property of linear operators to be in the surjective hull (injective hull) of the ideal of strictly singular (strictly cosingular) operators between Banach spaces is an interpolation property with respect to the real interpolation method with parameters 0 < ủ < 1 and < p < ℞.

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1 B. Beauzamy . Espaces d'Interpolation Reels: Topologie et Geometrie. Lecture Notes in Mathematics 666 (Berlin: Springer, 1978).

2 J. Bergh and J. Löiström . Interpolation Spaces - An Introduction. Grundlehren der mathematischen Wissenschaften 223 (Berlin: Springer, 1976).

3 J. Diestel . Sequences and Series in Banach Spaces. Graduate Texts in Mathematics 92 (Berlin: Springer, 1984).

4 J. Diestel . A survey of results related to the Dunford-Pettis property. Contemp. Math. 2 (1980), 1560.

7 K. Hayakawa . Interpolation by the real method preserves compactness of operators. J.Math. Soc. Japan 21 (1969), 189199.

8 T. Kato . Perturbation theory of nullity, deficiency and other quantities of linear operators. J. d' Analyse Math. 6 (1958), 261322.

9 J. L. Lions and J. Peetre . Sur une classe d'espaces d'interpolation. Instit. Hautes Etudes Sci. Pupl. Math. 19 (1964), 568.

12 A. Persson . Compact linear mappings between interpolation spaces. Arkiv Mat. 5 (1964), 215219.

13 H. Schechter . Quantities related to strictly singular operators. Indiana Univ. Math. J. 21 (1972), 10611071.

16 R. J. Whitley . Strictly singular operators and their conjugates. Trans. Amer. Math.Soc. 113 (1964), 252261.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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