Displaying similar documents to “On strictly singular operators”

On weakly infinite-dimensional subspuees

P. Borst (1992)

Fundamenta Mathematicae

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We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and d i m Y = ω 0 and d i m X = ω 0 + 1 . Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.

On linear operators having supercyclic vectors

Gerd Herzog (1992)

Studia Mathematica

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We show that for a real separable Banach space X there are operators in B(X) having supercyclic vectors if and only if dim X ≤ 2 or dim X = ∞.