A DOUBLY COMMUTING PAIR OF HYPONORMAL OPERATORS

Abstract

If ($H_1$, $H_2$) is a doubly commuting pair of hyponormal operators on a Hilbert spaces H, then there exists a commuting pair ($T_1$,$T_1$) of contractions on H such that $H_i$=$H_i^*$$T_i$ for each i=1,2.

Keywords

• hyponormal operators;
• doubly commuting;
• contractions

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References

1. Subnormal Operators J.B. Conway
2. Proc. Amer. Math. Soc. v.17 On majorization, factorization and range inclusion of operators on Hilbert space R. G. Douglas
3. A Hilbert Space Problem Book P. R. Halmos
4. Harmonic analysis of operators on Hilbert spaces B. Sz-Nagy;C. Foias