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Ideals in \(L(L_1)\)

  • W. B. JohnsonEmail author
  • G. Pisier
  • G. Schechtman
Article
  • 26 Downloads

Abstract

The main result is that there are infinitely many; in fact, a continuum; of closed (two-sided) ideals in the Banach algebra \(L(L_1)\) of bounded linear operators on \(L_1(0,1)\). This answers a question from Pietsch’s 1978 book “Operator Ideals”. The proof also shows that L(C[0, 1]) contains a continuum of closed ideals. Finally, a duality argument yields that \(L(\ell _\infty )\) has a continuum of closed ideals.

Mathematics Subject Classification

Primary 46B03 46B20 Secondary 46B28 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsWeizmann Institute of ScienceRehovotIsrael

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