Abstract
We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach space.MSC:47A15, 47H10.
Highlights
One of the most recalcitrant unsolved problems in operator theory is the invariant subspace problem
We refer the reader to the expository paper of Yadav [ ] for a detailed account of results related to the invariant subspace problem
In this survey we discuss some applications of fixed point theorems in the theory of invariant subspaces
Summary
One of the most recalcitrant unsolved problems in operator theory is the invariant subspace problem. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach space. In Section we consider the striking theorem of Lomonosov [ ] about the existence of invariant subspaces for algebras containing compact operators.
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