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On a Certain Operator Related to Blackwell’s Markov Chain

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  • Ernest Nieznaj

    (Lublin University of Technology)

Abstract

We present an example of a densely defined, linear operator on the $$l^{1}$$ l 1 space with the property that each basis vector of the standard Schauder basis of $$l^{1}$$ l 1 does not belong to its domain. Our example is based on the construction of a Markov chain with all states instantaneous given by D. Blackwell in 1958. In addition, it turns out that the closure of this operator is the generator of a strongly continuous semigroup of Markov operators associated with Blackwell’s chain.

Suggested Citation

  • Ernest Nieznaj, 2022. "On a Certain Operator Related to Blackwell’s Markov Chain," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1501-1510, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01110-8
    DOI: 10.1007/s10959-021-01110-8
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