Journal of the Mathematical Society of Japan

Domination of unbounded operators and commutativity

Jan STOCHEL and Franciszek Hugon SZAFRANIEC

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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.

Article information

J. Math. Soc. Japan, Volume 55, Number 2 (2003), 405-437.

First available in Project Euclid: 3 October 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.) 47B25: Symmetric and selfadjoint operators (unbounded) 44A60: Moment problems
Secondary: 47B20: Subnormal operators, hyponormal operators, etc. 43A35: Positive definite functions on groups, semigroups, etc.

Selfadjoint operator normal operator spectral commutativity symmetric operator formally normal operator subnormal operator domination relation


STOCHEL, Jan; Hugon SZAFRANIEC, Franciszek. Domination of unbounded operators and commutativity. J. Math. Soc. Japan 55 (2003), no. 2, 405--437. doi:10.2969/jmsj/1191419124.

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