Abstract/Details

Invariant subspaces for Banach space operators with a multiply connected spectrum


2006 2006

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Abstract (summary)

Ambrozie and Müller proved that the adjoint of a polynomially bounded operator whose spectrum contains the unit circle has a nontrivial invariant subspace. This result generalizes the well known result of Brown, Chevreau, and Pearcy which applies to Hilbert space contractions. We extend Ambrozie and Müller's result by proving an analogous result where the unit circle is replaced by the boundary of a multiply connected set. Indeed, we consider a multiply connected complex domain Ω = [special characters omitted] (λj, rj) where [special characters omitted] denotes the unit disk and (λ j, rj) ⊂ [special characters omitted] denotes the closed disk centered at λj with radius rj for j = 1,..., n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains ∂Ω and does not contain the points λ1, λ2,..., λn, such that for some constant k > 0 the inequalities ||p(T)|| ≤ k sup{|p(λ)| : |λ| ≤ 1} and || p(rj(T - λ jI)-1)|| ≤ k sup{| p(λ)| : |λ| ≤ 1} are satisfied for all polynomials p and j = 1,...,n, then there exists a nontrivial common invariant subspace for T* and ( T - λjI)*-1.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Banach space operators; Hilbert space contractions; Invariant subspaces; Multiply connected spectrum
Title
Invariant subspaces for Banach space operators with a multiply connected spectrum
Author
Yavuz, Onur
Number of pages
70
Publication year
2006
Degree date
2006
School code
0093
Source
DAI-B 67/06, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780542717512
Advisor
Bercovici, Hari
University/institution
Indiana University
University location
United States -- Indiana
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3219888
ProQuest document ID
305309986
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305309986
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