On product of projections

Mohammad Sal Moslehian

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 4, page 355-357
  • ISSN: 0044-8753

Abstract

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An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections.

How to cite

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Moslehian, Mohammad Sal. "On product of projections." Archivum Mathematicum 040.4 (2004): 355-357. <http://eudml.org/doc/249309>.

@article{Moslehian2004,
abstract = {An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections.},
author = {Moslehian, Mohammad Sal},
journal = {Archivum Mathematicum},
keywords = {projection; positive operator; factorization; positive operator; factorization},
language = {eng},
number = {4},
pages = {355-357},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On product of projections},
url = {http://eudml.org/doc/249309},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Moslehian, Mohammad Sal
TI - On product of projections
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 4
SP - 355
EP - 357
AB - An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections.
LA - eng
KW - projection; positive operator; factorization; positive operator; factorization
UR - http://eudml.org/doc/249309
ER -

References

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  1. Fong C. K., Wu P. Y., Diagonal operators: dilation, sum and product, Acta Sci. Math. (Szeged) 57 (1993), No. 1-4, 125–138. (1993) Zbl0819.47047MR1243273
  2. Halmos P. R., Products of shifts, Duke Math. J. 39 (1972), 779–787. (1972) Zbl0254.47038MR0313860
  3. Halmos P. R., Kakutani S., Products of symmetries, Bull. Amer. Math. Soc. 64 (1958), 77–78. (1958) Zbl0084.10602MR0100225
  4. Hawkins J. B., Kammerer W. J., A class of linear transformations which can be written as the product of projections, Proc. Amer. Math. Soc. 19 (1968), 739–745. (1968) MR0225195
  5. Phillips N. C., Every invertible Hilbert space operator is a product of seven positive operators, Canad. Math. Bull. 38 (1995), no. 2, 230–236. (1995) Zbl0826.46049MR1335103
  6. Radjavi H., On self-adjoint factorization of operators, Canad. J. Math. 21 (1969), 1421–1426. (1969) Zbl0188.44301MR0251575
  7. Radjavi H., Products of hermitian matrices and symmetries, Proc. Amer. Math. Soc. 21 (1969), 369–372; 26 (1970), 701. (1969) Zbl0175.30703MR0240116
  8. Wu P. Y., Product of normal operators, Canad. J. Math. XL, No 6 (1988), 1322–1330. (1988) MR0990101
  9. Wu P. Y., The operator factorization problems, Lin. Appl. 117 (1989), 35–63. (1989) Zbl0673.47018MR0993030

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