Journal article
Which subnormal Toeplitz operators are either normal or analytic?
Journal of functional analysis, Vol.263(8), pp.2333-2354
10/15/2012
DOI: 10.1016/j.jfa.2012.07.002
Abstract
We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmosʼs Problem 5: Which subnormal block Toeplitz operators are either normal or analytic? We extend and prove Abrahamseʼs theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol (i.e., a quotient of two bounded analytic functions), whose analytic and co-analytic parts have the “left coprime factorization”, is normal or analytic. We also prove that the left coprime factorization condition is essential. Finally, we examine a well-known conjecture, of whether every subnormal Toeplitz operator with finite rank self-commutator is normal or analytic.
Details
- Title: Subtitle
- Which subnormal Toeplitz operators are either normal or analytic?
- Creators
- Raúl E Curto - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USAIn Sung Hwang - Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of KoreaWoo Young Lee - Department of Mathematics, Seoul National University, Seoul 151-742, Republic of Korea
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.263(8), pp.2333-2354
- DOI
- 10.1016/j.jfa.2012.07.002
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Grant note
- DMS-0801168 / NSF 2009-0075890 / Korea government (MEST) 2010-0001983 / Korea government (MEST)
- Language
- English
- Date published
- 10/15/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985872102771
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