A bounded linear operator $T$ on a complex Banach space $\mathcal{X}$ is said to be full if $\overline{T\mathcal{M}}=\mathcal{M}$ for every invariant subspace $\mathcal{M}$ of $\mathcal{X}$. It is nearly full if $\overline{T\mathcal{M}}$ has finite codimension in $\mathcal{M}$. In this paper, we focus our attention to characterize full and nearly full operators in complex Banach spaces, showing that some valid results in complex Hilbert spaces can be generalized to this context.

In this paper we present a way to define a set of orthocenters for a triangle in the n-dimensional space R n and we will see some analogies of these orthocenters with the classic orthocenter of a triangle in the Euclidean plane.