Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 55, Number 2 (2003), 405-437.
Domination of unbounded operators and commutativity
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.
J. Math. Soc. Japan, Volume 55, Number 2 (2003), 405-437.
First available in Project Euclid: 3 October 2007
Permanent link to this document
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.
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. https://projecteuclid.org/euclid.jmsj/1191419124