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3 results

  • Normal Extensions of Representations of Abelian Semigroups

  • Boyu Li
  • Journal:
    Canadian Mathematical Bulletin / Volume 59 / Issue 3 / 01 September 2016
    Published online by Cambridge University Press:
    20 November 2018, pp. 564-574
    Print publication:
    01 September 2016
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  • A commuting family of subnormal operators need not have a commuting normal extension. We study when a representation of an abelian semigroup can be extended to a normal representation, and show that it suffices to extend the set of generators to commuting normals. We also extend a result due to Athavale to representations on abelian lattice ordered semigroups.

  • L(n)-HYPONORMALITY: A MISSING BRIDGE BETWEEN SUBNORMALITY AND PARANORMALITY

  • Part of
  • IL BONG JUNG, SUN HYUN PARK, JAN STOCHEL
  • Journal:
    Journal of the Australian Mathematical Society / Volume 88 / Issue 2 / April 2010
    Published online by Cambridge University Press:
    01 April 2010, pp. 193-203
    Print publication:
    April 2010
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  • A new notion of L(n)-hyponormality is introduced in order to provide a bridge between subnormality and paranormality, two concepts which have received considerable attention from operator theorists since the 1950s. Criteria for L(n)-hyponormality are given. Relationships to other notions of hyponormality are discussed in the context of weighted shift and composition operators.

  • On Quasisimilarity for Subnormal Operators, II

  • John B. Conway
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 1 / 01 March 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 37-40
    Print publication:
    01 March 1982
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  • Let S be a subnormal operator and let be the weak-star closed algebra generated by S and 1. An example of an irreducible cyclic subnormal operator S is found such that there is a T in with S and T quasisimilar but not unitarily equivalent. However, if S is the unilateral shift, T ∈ and S and T are quasisimilar, then S ≅ T.