Properties of mono-weakly hyponormal 2-variable weighted shifts

Abstract

In this paper, we study several properties for mono-weakly hyponormal 2-variable weighted shifts. First, we consider propagation phenomena for mono-weakly hyponormal (resp. mono-polynomially hyponormal) 2-variable weighted shifts. Next, we contemplate the mono-weak hyponormality under the Schur product. Finally, we study whether the mono-weak hyponormality is invariant under powers.

Keywords:

• Jointly hyponormal pairs
• subnormal pairs
• 2-variable weighted shifts
• flatness
• mono-weakly hyponormal
• mono-polynomially hyponormal
• Schur product

AMS Subject Classifications:

• Primary: 47B20
• 47B37
• 47A13
• Secondary: 44A60
• 47-04
• 47A20

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first named author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [grant number 2013R1A1A2011574].