Vol. 21, No. 3, 1967

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ISSN: 0030-8730
Invariant subspaces of polynomially compact operators on Banach space

Allen Richard Bernstein

Vol. 21 (1967), No. 3, 445–464
Abstract

This paper contains a proof of the following:

Main Theorem. Let T be a bounded linear operator on an infinite-dimensional Banach space B over the complex numbers. Suppose there exists a polynomial p(λ)0 with complex coefficients such that p(T) is compact (completely continuous). Then T leaves invariant at least one closed linear subspace of B other than {0} or B.

Mathematical Subject Classification
Primary: 47.35
Milestones
Received: 25 February 1966
Published: 1 June 1967
Authors
Allen Richard Bernstein