Authors:
Zoltán Sebestyén Department of Applied Analysis, Eötvös L. University, Pázmány Péter sétány 1/c, Budapest H-1117, Hungary

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Zsigmond Tarcsay Department of Applied Analysis, Eötvös L. University, Pázmány Péter sétány 1/c, Budapest H-1117, Hungary

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Abstract

We give an extension of a classical result due to Krein on biorthogonal expansions of compact operators which are symmetrizable with respect to a nondegenerate positive operator. Our approach makes essential use of the spectral expansion of an appropriate compact selfadjoint operator, the existence of which is due to Dieudonné.

  • [1] Dieudonné, J. 1961 Quasi-hermitian operators Proc. Internat. Sympos. Linear Spaces Jerusalem 1960 Jerusalem Academic Press Jerusalem 115122.

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  • [2] Douglas, R. G. 1966 On majorization, factorization, and range inclusion of operators on Hilbert space Proc. Amer. Math. Soc. 17 413415 .

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  • [3] Krein, M. G. 1998 Compact linear operators on functional spaces with two norms Integral Equations Operator Theory 30 140162 . Translated from Ukranian, dedicated to the memory of Mark Grigorievich Krein (1907–1989).

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  • [4] Sebestyén, Z. 1993 Operator extensions on Hilbert space Acta Sci. Math. (Szeged) 57 233248.

  • [5] Sebestyén, Z. 2000 Positivity of operator products Acta Sci. Math. (Szeged) 66 287294.

  • [6] Sebestyén, Z., Kapos, L. 1995 On range characterization of adjoint operators on Hilbert space Studia Sci. Math. Hungar. 30 261263.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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