论文标题
真实和积极操作员的嵌入性
Embeddability of real and positive operators
论文作者
论文摘要
将离散的马尔可夫链嵌入连续的链中是概率理论中著名的开放问题。受最近进步的启发，我们研究了实际和正面运算符的嵌入性问题与实际或正面$ C_0 $ - 序列的嵌入性问题，这些问题分别在有限和无限的可分离序列空间上。对于实际情况，我们提供了足够和必要的条件以嵌入。对于积极的操作员，我们提供了正面嵌入性的必要条件，包括$ 2 \ times 2 $ -case的完整说明。此外，我们表明，在$ \ ell^2 $上进行的真实收缩，实际嵌入性是典型的。
Embedding discrete Markov chains into continuous ones is a famous open problem in probability theory with many applications. Inspired by recent progress, we study the closely related questions of embeddability of real and positive operators into real or positive $C_0$-semigroups, respectively, on finite and infinite-dimensional separable sequence spaces. For the real case we give both sufficient and necessary conditions for embeddability. For positive operators we present necessary conditions for positive embeddability including a full description for the $2\times 2$-case. Moreover, we show that real embeddability is topologically typical for real contractions on $\ell^2$.
