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April, 2003 Domination of unbounded operators and commutativity
Jan STOCHEL, Franciszek Hugon SZAFRANIEC
J. Math. Soc. Japan 55(2): 405-437 (April, 2003). DOI: 10.2969/jmsj/1191419124


It is proved that pointwise commuting formally normal operators which are dominated by a single essentially normal operator are essentially normal and essentially spectrally commuting. The question when essential normality of a polynomial in an operator implies essential normality of that operator is solved in this way. Furthermore, domination by essentially normal powers of formally normal operators are studied and, as a consequence, extended versions of Nelson's criterion for essential spectral commutativity are proposed. Subsequent domination results ensuring joint subnormality of systems of operators are proved. Several applications to multidimensional moment problems are found.


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Jan STOCHEL. Franciszek Hugon SZAFRANIEC. "Domination of unbounded operators and commutativity." J. Math. Soc. Japan 55 (2) 405 - 437, April, 2003.


Published: April, 2003
First available in Project Euclid: 3 October 2007

zbMATH: 1037.47003
MathSciNet: MR1961294
Digital Object Identifier: 10.2969/jmsj/1191419124

Primary: 44A60 , 47B15 , 47B25
Secondary: 43A35 , 47B20

Keywords: domination relation , formally normal operator , normal operator , Selfadjoint operator , spectral commutativity , subnormal operator , ‎symmetric operator

Rights: Copyright © 2003 Mathematical Society of Japan


Vol.55 • No. 2 • April, 2003
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