One-sided star partial order preservers on \(B(H)\). (English) Zbl 07515572
Summary: Let \(B(H)\) be the algebra of all bounded linear operators on a complex Hilbert space \(H\). We classify (possibly non-additive) maps on \(B(H)\), with \(H\) infinite dimensional, which preserve either the left-star or the right-star partial order in both directions. We also introduce natural, weaker versions of these partial orders and classify their preservers.
MSC:
| 47B49 | Transformers, preservers (linear operators on spaces of linear operators) |
| 15A86 | Linear preserver problems |
| 06A06 | Partial orders, general |
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