Diagonal operators, s-numbers and Bernstein pairs
Abstract
Replacing the nested sequence of "finite" dimensional subspaces by the nested sequence of "closed" subspaces in the classical Bernstein lethargy theorem, we obtain a version of this theorem for the space of all bounded linear maps. Using this result and some properties of diagonal operators, we investigate conditions under which a suitable pair of Banach spaces form an exact Bernstein pair. We also show that many "classical" Banach spaces, including the couple form a Bernstein pair with respect to any sequence of s- numbers , for and .
DOI Code:
10.1285/i15900932v17p209
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