rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: On pairs of commuting operators
  name:
    name part: Ionescu, Adrian
    name part: 1962-
    role:
      role term: creator
  name:
    name part: Pearcy, Carl M.
    role:
      role term: degree supervisor.
  name:
    name part: Larson, David R.
    role:
      role term: degree committee member.
  name:
    name part: Smith, Roger
    role:
      role term: degree committee member.
  name:
    name part: Newton, Joseph
    role:
      role term: degree committee member.
  name:
    name part: Texas A & M University
    role:
      role term: degree granting institution.
  type of resource: text
  genre: bibliography
  genre: Academic theses
  origin info:
    place:
      place term: xx
    date issued: 1994
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: vii, 82 leaves ; 28 cm
  abstract: We investigate various problems associated w ith the structure theory of pairs of com m uting (polynom ially bounded) operators on H ilbert space. In particular, we develop a technique tha t enables us to expand the jo in t spectra of certain pairs of com m uting contractions, and we are able thereby to generalize some well-known results for the case of one contraction. We also present a connection between solving the invariant subspace problem fo r a single operator T on H ilb ert space and the existence of a common invariant subspace for two com m uting related operators. Thus, the problem of the existence of n o ntrivia l invariant subspaces for a single contraction w ith spectral radius one is reduced to the problem of the existence of n o n triv ia l common invariant subspaces for a p a ir of commuting contractions w ith rich jo in t spectra. We construct an H 00-functional calculus valid fo r certain pairs of commuting polynom ially bounded operators, based on the Briem -Davie-0ksendal construction of such a functional calculus for pairs o f com m uting completely nonunitary contractions, and we use dual algebra techniques in the direction of finding nontriv ia l common invariant subspaces for such pairs. In particular, we show that certain pairs o f absolutely continuous com m uting polynom ially bounded operators w ith rich jo in t spectrum have a large lattice o f common invariant subspaces.
  note: by Adrian Ionescu.
  note: Vita.
  note: "Major subject: Mathematics."
  note: Includes bibliographical references.
  note: Ph. D. Texas A & M University 1994
  subject:
    topic: Major mathematics
  identifier: http://proxy.library.tamu.edu/login
  related item:
    location:
      url: http://proxy.library.tamu.edu/login
  related item:
    location:
      url: http://proxy.library.tamu.edu/login
  record info:
    record content source: TXA
    record creation date: 960604
    record change date: 20200904152730.0
    record identifier: in00001299331
    language of cataloging:
      language term: eng