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Conditions under which all the bounded linear maps are compact

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Bibliography

  1. Banach, S.: Opérations Linéaires. New York: Chelsea 1955.

    Google Scholar 

  2. Bessaga, C., andA. Pełczyński: On bases and unconditional convergence in Banach spaces. Studia Math.17, 151–164 (1958).

    Google Scholar 

  3. Civin, P., andB. Yood: Quasi-reflexive spaces. Proc. Am. Math. Soc.8, 906–911 (1957).

    Google Scholar 

  4. Day, M.: Normed Linear Spaces. Berlin-Göttingen-Heidelberg: Springer 1958.

    Google Scholar 

  5. Dunford, N., andJ. Schwartz: Linear Operators Part I. New York: Interscience 1958.

    Google Scholar 

  6. Goldberg, S., andE. Thorp: On some open questions concerning strictly singular operators. Proc. Am. Math. Soc.14, 344–336 (1963).

    Google Scholar 

  7. Grothendieck, A.: Sur les applications linéaires faiblement compactes d'espaces du typeC (K). Canad. J. Math.5, 129–173 (1953).

    Google Scholar 

  8. Kato, T.: Perturbation theory for nullity, deficiency and other quantities of linear operators. J. d'Analyse Math.6, 261–322 (1958).

    Google Scholar 

  9. Pełczyński, A.: Projections in certain Banach spaces. Studia Math.19, 209–228 (1960).

    Google Scholar 

  10. Phillips, R.: On linear transformations. Trans. Am. Math. Soc.48, 516–541 (1940).

    Google Scholar 

  11. Taylor, A.: Introduction to Functional Analysis. New York: Wiley 1958.

    Google Scholar 

  12. Whitley, R.: Strictly singular operators and their conjugates. Trans. Am. Math. Soc.113, 252–261 (1964).

    Google Scholar 

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Authors and Affiliations

  1. University Park, New Mexico, USA

    Elton Lacey & R. J. Whitley

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  1. Elton Lacey
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  2. R. J. Whitley
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Additional information

The first author was partially supported by the National Science Foundation under research grant NSF-G 25058 and the second under a National Science Foundation Cooperative Fellowship.

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Lacey, E., Whitley, R.J. Conditions under which all the bounded linear maps are compact. Math. Ann. 158, 1–5 (1965). https://doi.org/10.1007/BF01370391

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