Journal article
Hyponormality and subnormality for powers of commuting pairs of subnormal operators
Journal of functional analysis, Vol.245(2), pp.390-412
2007
DOI: 10.1016/j.jfa.2007.01.002
Abstract
Let H 0 (respectively H ∞ ) denote the class of commuting pairs of subnormal operators on Hilbert space (respectively subnormal pairs), and for an integer k ⩾ 1 let H k denote the class of k-hyponormal pairs in H 0 . We study the hyponormality and subnormality of powers of pairs in H k . We first show that if ( T 1 , T 2 ) ∈ H 1 , the pair ( T 1 2 , T 2 ) may fail to be in H 1 . Conversely, we find a pair ( T 1 , T 2 ) ∈ H 0 such that ( T 1 2 , T 2 ) ∈ H 1 but ( T 1 , T 2 ) ∉ H 1 . Next, we show that there exists a pair ( T 1 , T 2 ) ∈ H 1 such that T 1 m T 2 n is subnormal (for all m , n ⩾ 1 ), but ( T 1 , T 2 ) is not in H ∞ ; this further stretches the gap between the classes H 1 and H ∞ . Finally, we prove that there exists a large class of 2-variable weighted shifts ( T 1 , T 2 ) (namely those pairs in H 0 whose cores are of tensor form (cf. Definition 3.4)), for which the subnormality of ( T 1 2 , T 2 ) and ( T 1 , T 2 2 ) does imply the subnormality of ( T 1 , T 2 ) .
Details
- Title: Subtitle
- Hyponormality and subnormality for powers of commuting pairs of subnormal operators
- Creators
- Raúl E Curto - Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USASang Hoon Lee - Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USAJasang Yoon - Department of Mathematics, Iowa State University, Ames, IA 50011, USA
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.245(2), pp.390-412
- DOI
- 10.1016/j.jfa.2007.01.002
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2007
- Academic Unit
- Mathematics
- Record Identifier
- 9983985856602771
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