The pair (c₀, c₀) fails the Compact Perturbation Property for the minimum modulus, as a rank-one compact perturbation strictly increases the minimum modulus of a non-min-attaining operator.
and Mart´ ınez-Cervantes, G.Some remarks on the weak maximizing property, J
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For separable infinite-dimensional Banach spaces, the weak minimizing property holds precisely when X is reflexive and Y contains no isomorphic copy of X, up to equivalent renorming of Y.
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Weak Minimizing Property and the Compact Perturbation Property for the Minimum Modulus
The pair (c₀, c₀) fails the Compact Perturbation Property for the minimum modulus, as a rank-one compact perturbation strictly increases the minimum modulus of a non-min-attaining operator.
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Weak minimizing property and reflexivity
For separable infinite-dimensional Banach spaces, the weak minimizing property holds precisely when X is reflexive and Y contains no isomorphic copy of X, up to equivalent renorming of Y.