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 language | English |
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Pages (from-to) | 76-86 |
Number of pages | 11 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 380 |
Issue number | 1 |
DOIs | |
State | Published - 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: [email protected] (S. Jung), [email protected] (E. Ko), [email protected] (M. Lee).
Keywords
- (p,k)-Quasihyponormal operator
- Algebraic operator
- Invariant subspace
- P-Hyponormal operator
- Subscalar operator