On a Certain Operator Related to Blackwell’s Markov Chain

Ernest Nieznaj ()
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Ernest Nieznaj: Lublin University of Technology

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1501-1510

Abstract: 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.

Keywords: Blackwell’s example; Markov semigroup; unbounded operator; 47D07; 60J27; 60J35 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01110-8

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