论文标题
功能模型达到相似性和$ a $ - 扣除
Functional models up to similarity and $a$-contractions
论文作者
论文摘要
我们将$ m $ isometries和$ m $ - 债券（用于正整数$ m $）的概括对我们称为$ a $ isometries和$ a $ a-a-a $ nartions的概括。我们表明，任何希尔伯特太空运营商都满足某些阶级的不平等（以遗传形式），都类似于$ a $ cartract。该结果基于一些Banach代数技术，是最后两位作者最近结果的改进。我们还证明，如果$ b <a $，任何$ a $ a $ contraction $ t $都是$ b $ - 征收，并且对$ t^n x $的规范的增长施加了额外的条件，其中$ x $是任意的矢量。在这里，我们使用分数有限差异的一些属性。
We study the generalization of $m$-isometries and $m$-contractions (for positive integers $m$) to what we call $a$-isometries and $a$-contractions for positive real numbers $a$. We show that any Hilbert space operator, satisfying an inequality of certain class (in hereditary form), is similar to $a$-contractions. This result is based on some Banach algebras techniques and is an improvement of a recent result by the last two authors. We also prove that any $a$-contraction $T$ is a $b$-contraction, if $b<a$ and one imposes an additional condition on the growth of the norms of $T^n x$, where $x$ is an arbitrary vector. Here we use some properties of fractional finite differences.
