Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica
Doi
Abstract
Berkani and Kachad [18], [19], and Sanabria et al. [32], introduced and studied
strong variations of Weyl type Theorems. In this paper, we study the behavior of these
strong variations of Weyl type theorems for an operator T on a proper closed and Tinvariant subspace W ⊆ X such that T
n
(X) ⊆ W for some n ≥ 1, where T ∈ L(X) and
X is an infinite-dimensional complex Banach space. The main purpose of this paper is to
prove that for these subspaces (which generalize the case T
n
(X) closed for some n ≥ 0),
these strong variations of Weyl type theorems are preserved from T to its restriction on W
and vice-versa. As consequence of our results, we give sufficient conditions for which these
strong variations of Weyl type Theorems are equivalent for two given operators. Also, some
applications to multiplication operators acting on the boundary variation space BV [0, 1]
are given