Ideals of operators strictly singular on subspaces
HTML articles powered by AMS MathViewer
- by Michael J. Meyer PDF
- Proc. Amer. Math. Soc. 122 (1994), 1121-1123 Request permission
Abstract:
For each set $\Omega$ of cardinality at most ${2^\omega }$, we give an easy construction of Banach spaces X, such that the algebra $\mathcal {B}(X)$ of all bounded linear operators on X contains a lattice of closed ideals, which is order isomorphic with respect to inclusion to the full power set of $\Omega$.References
- Horacio Porta, Two sided ideals of operators, Bull. Amer. Math. Soc. 75 (1969), 599–602. MR 239433, DOI 10.1090/S0002-9904-1969-12254-8
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 1121-1123
- MSC: Primary 47D50; Secondary 46H10, 47B99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1219729-8
- MathSciNet review: 1219729