Closed ideals in the Banach algebra of operators on a Banach space

• Autorzy: Niels Jakob Laustsen , Richard J. Loy
• Języki publikacji: EN

Abstrakty

EN

In general, little is known about the lattice of closed ideals in the Banach algebra ℬ(E) of all bounded, linear operators on a Banach space E. We list the (few) Banach spaces for which this lattice is completely understood, and we give a survey of partial results for a number of other Banach spaces. We then investigate the lattice of closed ideals in ℬ(F), where F is one of Figiel's reflexive Banach spaces not isomorphic to their Cartesian squares. Our main result is that this lattice is uncountable.

Kategorie tematyczne

• 46H10: Ideals and subalgebras
• 47L20: Operator ideals
• 47L10: Algebras of operators on Banach spaces and other topological linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 67
• Numer: 1
• Strony: 245-264

Daty

wydano

2005

Twórcy

autor

Niels Jakob Laustsen

• Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

autor

Richard J. Loy

• Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia

Identyfikatory

DOI

10.4064/bc67-0-20