In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded operator on a complex Banach space sends some non-trivial closed subspace to itself. Xis said to be T-invariant if T(S) S. A vector subspace Mof Xwhich is T-invariant is called an invariant subspace for T. The subspaces f0gand Xare obviously invariant under T; these are referred to as trivial invariant subspaces. The problem, in a general form, is stated as follows: The Invariant Subspace Problem. o \On the invariant subspace problem for Banach spaces", Acta Math. (), no. , In the Banach space setting In , P. En o showed in the Seminaire Maurey-Schwartz at the Ecole Polytechnique in Par s: There exists a separable Banach space Band a linear, bounded.

# Invariant subspace problem pdf

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