Quasi-invariant subspaces generated by polynomials with nonzero leading terms
Volume 164 / 2004
Studia Mathematica 164 (2004), 231-241
MSC: 46J15, 46H25, 47A15.
DOI: 10.4064/sm164-3-2
Abstract
We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace $[p]$ generated by a polynomial $p$ with nonzero leading term, a quasi-invariant subspace $M$ is similar to $[p]$ if and only if there exists a polynomial $q$ with the same leading term as $p$ such that $M=[q].$
