Virginia Tech
    • Log in
    View Item 
    •   VTechWorks Home
    • ETDs: Virginia Tech Electronic Theses and Dissertations
    • Doctoral Dissertations
    • View Item
    •   VTechWorks Home
    • ETDs: Virginia Tech Electronic Theses and Dissertations
    • Doctoral Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Functions of subnormal operators

    Thumbnail
    View/Open
    LD5655.V856_1982.M544.pdf (2.338Mb)
    Downloads: 127
    Date
    1982
    Author
    Miller, Thomas L.
    Metadata
    Show full item record
    Abstract
    If f is analytic in a neighborhood of ∂D = {z| |z|= 1} and if K = f(∂D), then C-K has only finitely many components; moreover, if U is a bounded simply connected region of the plane, then ∂U = Uj=0nj where each rj is a rectifiable Jordan curve and ri ∩ rj is a finite set whenever i ≠ j. Let μ be a positive regular Borel measure supported on ∂D and let m denote normalized Lebesgue measure on ∂D. If L is a compact set such that ∂L ⊂ K and R(L) is a Dirichlet algebra and if ν = μof⁻¹, then the Lebesgue decomposition of ν|∂V with respect to harmonic measure for L is ν|∂V = μaof⁻¹|∂V + μsof⁻¹|∂V where V = intL and μ = μa + μs is the Lebesgue decomposition of μ with respect to m. Applying Sarason’s process, we obtain P∞(ν) ≠ L∞(ν) if, and only if there is a Jordan curve r contained in K such that mof⁻¹|Γ << μaof⁻¹|Γ. If U is a unitary operator with scalar-valued spectral measure μ then f(U) is non-reductive if and only if there is a Jordan curve r ⊂ K such that mof⁻¹|Γ << μaof⁻¹|Γ. Let G be a bounded region of the plane and B(H) the algebra of bounded operators in the separable Hilbert space H. If π: H∞(G)→B(H) is a norm-continuous homomorphism such that π(1) = 1 and π(z) is pure subnormal then π is weak-star, weak-star continuous. Moreover, if S is a pure subnormal contraction, the S*n→0 sot.
    URI
    http://hdl.handle.net/10919/80999
    Collections
    • Doctoral Dissertations [16337]

    If you believe that any material in VTechWorks should be removed, please see our policy and procedure for Requesting that Material be Amended or Removed. All takedown requests will be promptly acknowledged and investigated.

    Virginia Tech | University Libraries | Contact Us
     

     

    VTechWorks

    AboutPoliciesHelp

    Browse

    All of VTechWorksCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Log inRegister

    Statistics

    View Usage Statistics

    If you believe that any material in VTechWorks should be removed, please see our policy and procedure for Requesting that Material be Amended or Removed. All takedown requests will be promptly acknowledged and investigated.

    Virginia Tech | University Libraries | Contact Us