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Finite representability and super-ideals of operators

Stefan Heinrich — 1980

CONTENTSIntroduction............................................................................... 5Notation............................................................................................. 61. Finite representability of operators.......................................... 72. Super-ideals of operators......................................................... 143. Connections with Banach space theory................................. 204. Procedures on super-ideals........................................................

On the randomized complexity of Banach space valued integration

Stefan Heinrich;  Aicke Hinrichs — 2014

Studia Mathematica

We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by c n - r / d - 1 + 1 / p if and only if X is of equal norm type p.

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