Ideals in L(L1)

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...

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Veröffentlicht in:	Mathematische annalen 2020-02, Vol.376 (1-2), p.693-705
Hauptverfasser:	Johnson, W. B., Pisier, G., Schechtman, G.
Format:	Artikel
Sprache:	eng
Schlagworte:	Banach spaces Linear operators Mathematics Mathematics and Statistics Operators (mathematics)
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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 ( ℓ ∞ ) has a continuum of closed ideals.
ISSN:	0025-5831 1432-1807
DOI:	10.1007/s00208-019-01934-0