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(2001 / vol.4 / no.2)
Bridges between hyponormal and subnormal operators
Il Bong Jung
Pages. 119-126     



There are several bridges to detect the gap between subnormal and hyponormal operators on a Hilbert space. In this article we first discuss a bridge through the classes of (strongly) $k$-hyponormal operators. Another bridge can be obtained through the classes of weakly $k$-hyponormal operators. To detect those bridges, we consider weighted shifts and their backward extensions with variables. In particular, we discuss quadratically hyponormal and cubically hyponormal weighted shifts and introduce some related open problems.



$k$-hyponormal weighted shifts, quadratically hyponormal weighted shifts, cubically hyponormal weighted shifts, polynomially hyponormal weighted shifts



47B20, 47B37