A remark concerning Putinar's model of hyponormal weighted shifts

Vasile Lauric

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 4, page 1125-1130
  • ISSN: 0011-4642

Abstract

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The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.

How to cite

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Lauric, Vasile. "A remark concerning Putinar's model of hyponormal weighted shifts." Czechoslovak Mathematical Journal 68.4 (2018): 1125-1130. <http://eudml.org/doc/294598>.

@article{Lauric2018,
abstract = {The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.},
author = {Lauric, Vasile},
journal = {Czechoslovak Mathematical Journal},
keywords = {weighted shift operator; almost normal operator; hyponormal operator},
language = {eng},
number = {4},
pages = {1125-1130},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A remark concerning Putinar's model of hyponormal weighted shifts},
url = {http://eudml.org/doc/294598},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Lauric, Vasile
TI - A remark concerning Putinar's model of hyponormal weighted shifts
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 1125
EP - 1130
AB - The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.
LA - eng
KW - weighted shift operator; almost normal operator; hyponormal operator
UR - http://eudml.org/doc/294598
ER -

References

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  1. Lauric, V., Remarks on hyponormal operators and almost normal operators, Matematiche (Catania) 72 (2017), 3-8. (2017) MR3666546
  2. Pasnicu, C., Weighted shifts as direct summands mod 𝒞 2 of normal operators, Dilation Theory, Toeplitz operators, and Other Topics 7th Int. Conf. Oper. Theory, Timisoara, 1982, Oper. Theory, Adv. Appl. (1983) 275-281. Zbl0527.47021MR0789643
  3. Putinar, M., Hyponormal operators are subscalar, J. Oper. Theory 12 (1984), 385-395. (1984) Zbl0573.47016MR0757441
  4. Voiculescu, D., Hilbert space operators modulo normed ideals, Proc. Int. Congr. Math. Warszawa, 1983 2 (1984), 1041-1047. (1984) Zbl0594.46063MR0804756
  5. Voiculescu, D. V., 10.4171/JNCG/181, J. Noncommut. Geom. 8 (2014), 1123-1145. (2014) Zbl1325.46074MR3310942DOI10.4171/JNCG/181

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