Subscalarity of (p,k)-quasihyponormal operators

Sungeun Jung, Eungil Ko, Mee Jung Lee

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5 Scopus citations

Abstract

In this paper, we show that every (p,k)-quasihyponormal operator has a scalar extension and give some spectral properties of the scalar extensions of (p,k)-quasihyponormal operators. As a corollary, we get that such an operator with rich spectrum has a nontrivial invariant subspace. Finally, we prove that the sum of a p-hyponormal operator and an algebraic operator which are commuting is subscalar.

Original languageEnglish
Pages (from-to)76-86
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume380
Issue number1
DOIs
StatePublished - 1 Aug 2011

Bibliographical note

Funding Information:
✩ This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). * Corresponding author. E-mail addresses: ssung105@ewhain.net (S. Jung), eiko@ewha.ac.kr (E. Ko), meejung@ewhain.net (M. Lee).

Keywords

  • (p,k)-Quasihyponormal operator
  • Algebraic operator
  • Invariant subspace
  • P-Hyponormal operator
  • Subscalar operator

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