Let $A$ be an operator on a Banach space, possibly unbounded, such that its resolvent $(\lambda - A)^{-1}$ is compact. Is $A$ then a Fredholm operator of index 0? My feeling is yes but I cannot prove it.
Thank you for the help.
Let $A$ be an operator on a Banach space, possibly unbounded, such that its resolvent $(\lambda - A)^{-1}$ is compact. Is $A$ then a Fredholm operator of index 0? My feeling is yes but I cannot prove it.
Thank you for the help.