• Find People
  • Campus Map
  • PiratePort
  • A-Z
    • About
    • Submit
    • Browse
    • Login
    View Item 
    •   ScholarShip Home
    • Other Campus Research
    • Open Access
    • View Item
    •   ScholarShip Home
    • Other Campus Research
    • Open Access
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of The ScholarShipCommunities & CollectionsDateAuthorsTitlesSubjectsTypeDate SubmittedThis CollectionDateAuthorsTitlesSubjectsTypeDate Submitted

    My Account

    Login

    Statistics

    View Google Analytics Statistics

    Compact operators and nest representations of limit algebras

    Thumbnail
    View/ Open
    Main Article (279.2Kb)

    Show full item record
    
    Author
    Katsoulis, Elias; Peters, Justin R.
    Abstract
    In this paper we study the nest representations $ \rho: \mathcal{A} \longrightarrow \operatorname{Alg} \mathcal{N}$ of a strongly maximal TAF algebra $ \mathcal{A}$, whose ranges contain non-zero compact operators. We introduce a particular class of such representations, the essential nest representations, and we show that their kernels coincide with the completely meet irreducible ideals. From this we deduce that there exist enough contractive nest representations, with non-zero compact operators in their range, to separate the points in $ \mathcal{A}$. Using nest representation theory, we also give a coordinate-free description of the fundamental groupoid for strongly maximal TAF algebras. For an arbitrary nest representation $ \rho: \mathcal{A} \longrightarrow \operatorname{Alg} \mathcal{N}$, we show that the presence of non-zero compact operators in the range of $ \rho$ implies that $ \mathcal{N}$ is similar to a completely atomic nest. If, in addition, $ \rho (\mathcal{A} )$ is closed, then every compact operator in $ \rho (\mathcal{A} )$ can be approximated by sums of rank one operators $ \rho (\mathcal{A} )$. In the case of $ \mathbb{N}$-ordered nest representations, we show that $ \rho ( \mathcal{A})$ contains finite rank operators iff $ \ker \rho $ fails to be a prime ideal.
    URI
    http://hdl.handle.net/10342/8912
    Subject
    algebra compact operators nest representations
    Date
    2007-01-04
    Citation:
    APA:
    Katsoulis, Elias, & Peters, Justin R.. (January 2007). Compact operators and nest representations of limit algebras. Transactions of the American Mathematical Society, (359:6), p.2721-2739. Retrieved from http://hdl.handle.net/10342/8912

    Display/Hide MLA, Chicago and APA citation formats.

    MLA:
    Katsoulis, Elias, and Peters, Justin R.. "Compact operators and nest representations of limit algebras". Transactions of the American Mathematical Society. 359:6. (2721-2739.), January 2007. August 13, 2022. http://hdl.handle.net/10342/8912.
    Chicago:
    Katsoulis, Elias and Peters, Justin R., "Compact operators and nest representations of limit algebras," Transactions of the American Mathematical Society 359, no. 6 (January 2007), http://hdl.handle.net/10342/8912 (accessed August 13, 2022).
    AMA:
    Katsoulis, Elias, Peters, Justin R.. Compact operators and nest representations of limit algebras. Transactions of the American Mathematical Society. January 2007; 359(6) 2721-2739. http://hdl.handle.net/10342/8912. Accessed August 13, 2022.
    Collections
    • Open Access

    xmlui.ArtifactBrowser.ItemViewer.elsevier_entitlement

    East Carolina University has created ScholarShip, a digital archive for the scholarly output of the ECU community.

    • About
    • Contact Us
    • Send Feedback