Embeddability of real and positive operators. (English) Zbl 1522.47040
The problem of embedding a discrete object into a continuous one with the same properties appears in many forms and has been studied in many papers. In the present paper, the authors consider embeddability in the context of real and positive bounded linear operators. By real operators, they mean operators on complexifications of real Banach spaces which map real vectors to real vectors. While the authors investigate real embeddability for general bounded linear operators on Banach spaces, in their study of positive embeddability they restrict their considerations to finite and infinite matrices. In the end, it is shown that, contrary to the finite-dimensional case, real embeddability is typical for infinite matrices.
Reviewer: Anatoliy Swishchuk (Calgary)
MSC:
| 47B01 | Operators on Banach spaces |
| 47B65 | Positive linear operators and order-bounded operators |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
Keywords:
embedding problem; real operators; positive operators; infinite matrices; strongly continuous semigroupsSoftware:
mftoolboxReferences:
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