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On interpolation of strictly (co-)singular linear operators

  • O. J. Beucher (a1)
Abstract
Synopsis

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).

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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.

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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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