Author/Authors :
Aghasizadeh، T. نويسنده Ferdowsi University of Mashhad , , Hejazian، S. نويسنده Ferdowsi University of Mashhad ,
Abstract :
Let $\mathcal L(\mathcal B(\mathcal H))$ be the algebra of all linear operators on
$\mathcal B(\mathcal H)$ and $\mathcal P$ be a property on
$\mathcal B(\mathcal H)$. For $\phi_{1},\phi_{2}\in \mathcal
L(\mathcal B(\mathcal H))$, we say that
$\phi_{1}{\sim}_{_{\mathcal P}} \phi_{2}$, whenever $\phi_{1}(T) $
has property $\mathcal P$, if and only if $\phi_{2}(T)$ has this
property. In particular, if $\mathcal I$ is the identity map on
$\mathcal B(\mathcal H)$, then $\phi{\sim}_{_{\mathcal P}}
\mathcal I$ means that $\phi$ preserves property $\mathcal P$ in
both directions. Each property $\mathcal P$ produces an
equivalence relation on $\mathcal L(\mathcal B(\mathcal H))$. We
study the relation between equivalence classes with respect to
different properties such as being Fredholm, semi-Fredholm,
compact, finite rank, generalized invertible, or having a
specific semi-index.
