Order ideals and ring ideals. (English) Zbl 0711.47020
Riesz spaces, positive operators and applications, Proc. Conf., Oxford/MS (USA) 1986, 1-3 (1986).
Summary: [For the entire collection see Zbl 0701.00017.]
Relations between
The ring ideal ring(T) generated by a continuous operator T: \(X\to Y\) between Banach spaces
and the order ideal \({\mathcal A}_ T=\{S: E\to F;\) \(| S| \leq n(T)\) for some \(n\}\) of a regular operator \(T:E\to F\) between Banach lattices, F being Dedekind complete,
are considered. No proofs.
Relations between
The ring ideal ring(T) generated by a continuous operator T: \(X\to Y\) between Banach spaces
and the order ideal \({\mathcal A}_ T=\{S: E\to F;\) \(| S| \leq n(T)\) for some \(n\}\) of a regular operator \(T:E\to F\) between Banach lattices, F being Dedekind complete,
are considered. No proofs.
MSC:
| 47B65 | Positive linear operators and order-bounded operators |
| 46A40 | Ordered topological linear spaces, vector lattices |
| 46B42 | Banach lattices |
