We present an example of a densely defined, linear operator on the \(l^{1}\) space with the property that each basis vector of the standard Schauder basis of \(l^{1}\) 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.

中文翻译：

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与布莱克威尔马尔可夫链相关的某算子

我们提出在一个稠定，线性算子的一个例子\（L ^ {1} \）与属性空间的标准Schauder基的每个基矢量\（L ^ {1} \）不属于它的领域。我们的例子是基于 D. Blackwell 在 1958 年给出的所有状态瞬时的马尔可夫链的构造。此外，事实证明，这个算子的闭包是与布莱克威尔链相关联的马尔可夫算子的强连续半群的生成器.