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Functional models up to similarity and $a$-contractions
- Publication Year :
- 2020
-
Abstract
- 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.<br />Comment: 26 pages
- Subjects :
- Mathematics - Functional Analysis
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2005.00075
- Document Type :
- Working Paper