Integral Equations and Operator Theory

, Volume 59, Issue 2, pp 173–187

Kth Roots of p-Hyponormal Operators are Subscalar Operators of Order 4k

Article

DOI: 10.1007/s00020-007-1519-8

Cite this article as:
Ko, E. Integr. equ. oper. theory (2007) 59: 173. doi:10.1007/s00020-007-1519-8

Abstract.

In this paper, we consider the special case of the question raised by Halmos (see below). In particular, we show that if Tk is p-hyponormal, then T is a subscalar operator of order 4k. As a corollary, we obtain that if Tk is p-hyponormal and σ(T) has nonempty interior in the plane, then T has a nontrivial invariant subspace.

Mathematics Subject Classification (2000).

47B20 47B38 

Keywords.

p-hyponormality subscalarity the property (βinvariant subspace 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of MathematicsEwha Women’s UniversitySeoulKorea

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