DIVISIBLE SUBSPACES OF LINEAR OPERATORS ON BANACH SPACES

DIVISIBLE SUBSPACES OF LINEAR OPERATORS ON BANACH SPACES

In this paper, we investigate the properties related to algebraic spectral subspaces and divisible subspaces of linear operators on a Banach space. In addition, using the concept of topological divisior of zero of a Banach algebra, we prove that the only closed divisible subspace of a bounded linear operator on a Banach space is trivial. We also give an example of a bounded linear operator on a Banach space with non-trivial divisible subspaces.

1. Algebraic spectral subspaces of linear operators

2. Divisible subspaces of linear operators

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