Abstract
AbstractLet $${{\mathcal {S}}}{{\mathcal {S}}}$$
S
S
and $${{\mathcal {S}}}{{\mathcal {C}}}$$
S
C
be the strictly singular and the strictly cosingular operators acting between Banach spaces, and let $$P\Phi _+$$
P
Φ
+
and $$P\Phi _+$$
P
Φ
+
be the perturbation classes for the upper and the lower semi-Fredholm operators. We study two classes of operators $$\Phi {\mathcal {S}}$$
Φ
S
and $$\Phi {\mathcal {C}}$$
Φ
C
that satisfy $${{\mathcal {S}}}{{\mathcal {S}}}\subset \Phi {\mathcal {S}}\subset P\Phi _+$$
S
S
⊂
Φ
S
⊂
P
Φ
+
and $${{\mathcal {S}}}{{\mathcal {C}}}\subset \Phi {\mathcal {C}}\subset P\Phi _-.$$
S
C
⊂
Φ
C
⊂
P
Φ
-
.
We give some conditions under which these inclusions become equalities, from which we derive some positive solutions to the perturbation classes problem for semi-Fredholm operators.
Funder
Ministerio de Ciencia, Innovación y Universidades
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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