Bulletin of the
Korean Mathematical Society BKMS

Let $H$ and $K$ be two Hilbert spaces, and let $A$ and $B$ be two bounded linear operators from $H$ to $K$. We are interested in Range$B^\ast \supseteq$ Range$A^\ast $. It is well known that this is equivalent to the inequality $A^\ast A\geq\varepsilon B^\ast B$ for a positive constant $\varepsilon$. We study conditions in terms of symbols when $A$ and $B$ are singular integral operators, Hankel operators or Toeplitz operators, etc.

Keywords: singular integral operator, Hankel operator, Toeplitz operator, range inclusion

MSC numbers: Primary 47B35