Models

Carlos S. Kubrusly
Additional contact information
Carlos S. Kubrusly: Catholic University — PUC/RJ

Chapter Chapter 6 in An Introduction to Models and Decompositions in Operator Theory, 1997, pp 87-100 from Springer

Abstract: Abstract An operator is said to be a universal model if every operator in B[H] is similar to a multiple of a part of it. Drop “universal” by constraining the definition to a class of operators: an operator is a model for a class of operators in B[H] if every operator in that class is similar to a multiple of a part of it. Equivalently (see Proposition 1.1), if every operator in that class is a part of an operator similar to a multiple of it. An operator is an extension of an operator T ∈ B[H] if T is a part of it. We shall say that a class P of operators is a pattern for a class C in B[H] if every operator in C has an extension in P (i.e. if every operator in C is a part of an operator in P). For instance, normal operators are patterns for subnormal operators (by the very definition of subnormal operators), bilateral shifts are patterns for unilateral shifts (cf. Lemma 2.14), and unitaries are patterns for isometries (according to Lemma 5.7). Thus an operator is a model for a class of operators C in B[H] if the class of all operators similar to a multiple of it is a pattern for C. Every uniformly stable operator is similar to a part of a canonical backward unilateral shift.

Keywords: Hilbert Space; Invariant Subspace; Spectral Radius; Universal Model; Strong Stability (search for similar items in EconPapers)
Date: 1997
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1998-9_7

Ordering information: This item can be ordered from
http://www.springer.com/9781461219989

DOI: 10.1007/978-1-4612-1998-9_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().