Some invariant subspaces for w-hyponormal operators - Rashid, M. H. M. (Linear & multilinear algebra, 2019)
In this paper, we prove that if is w-hyponormal, then the quasinilpotent part of T is given by for all sufficiently large integers p, where . We prove that if T is w-hyponormal and the spectrum is finite, then T is algebraic. In addition, we prove that if is w-hyponormal and has decomposition property , then T has a non-trivial invariant closed linear subspace. Also, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for w-hyponormal operators.