ACTA issues

## Structure of semi-Fredholm operators with fixed nullity

Haikel Skhiri

Acta Sci. Math. (Szeged) 63:3-4(1997), 607-622
5786/2009

 Abstract. We show that the set $\cup_{j\in J}F^n_j$ is arcwise connected, where $J$ is a subset of $\overline{\msbm N}$ and $F^n_j (n\leq j)$ is the set of semi-Fredholm operators of index $n$ and kernel dimension $j$. The distance of an arbitray operator to $\cup_{j\in J}F^n_j$ is also determined. We show that dist($T,\cup_{j\in J}F^n_j )=$ dist$(T, F^n_{j_0})$, where $j_0 =$ inf$\{j: j \in J\}$. Thus $F^n_{j_0}$ is dense in $\cup_{j\in J}F^n_j$. We also find the boundary of $\cup_{j\in J}F^n_j$ and $\overline{\cup_{j\in J}F^n_j }$. AMS Subject Classification (1991): 47A53 Received March 10, 1997. (Registered under 5786/2009.)