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

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Laustsen N., Loy R.

Banach Center Publications

2005

tom 67

nr 1

245-264

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.

Ograniczanie wyników

1 Banach Center Publications

1 Laustsen N.

1 Loy R.

1 2005

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