Operators on a finite dimensional space

  • Ko, Eungil (Department of Mathematics, Ewha Women's University)
  • Published : 1997.02.01

Abstract

Let $H$ and $K$ be separable, complex Hilbert spaces and $L(H, K)$ denote the space of all linear, bounded operators from $H$ to $K$. If $H = K$, we write $L(H)$ in place of $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$ T^*h \right\$\mid$ \leq \left\$\mid$ Th \right\$\mid$$ for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

References

  1. Subnormal operators J. B. Conway
  2. Ph.D. thesis, Indiana University Subscalar and quasisubscalar operators Eungil Ko
  3. J. Operator Theory v.12 Hyponormal operators are subscalar M. Putinar
  4. Invariant subspaces H. Radjavi;P. Rosenthal