We study the rank of complex skew symmetric operators on separable Hilbert spaces. We prove that a finite rank complex skew symmetric operator can't have an odd rank. As applications, we show that any finite rank commutator of two Toeplitz operators on the pluriharmonic Bergman space of the ball can't have an odd rank. We also show that for any positive even integer N, there are two Toeplitz operators whose commutator is exactly of rank N. Also we obtain the similar result for certain truncated Toeplitz operators.
|Number of pages||14|
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2015 May 15|
- Complex skew symmetric operators
- Toeplitz operators
ASJC Scopus subject areas
- Applied Mathematics