This article is cited in 3 papers

Rate of Decay of the Bernstein Numbers

A. Plichko

Department of Mathematics, Cracow University of Technology, Cracow, Poland

Abstract: We show that if a Banach space $X$ contains uniformly complemented $\ell_2^n$'s then there exists a universal constant $b=b(X)>0$ such that for each Banach space $Y$, and any sequence $d_n\downarrow 0$ there is a bounded linear operator $T:X\to Y$ with the Bernstein numbers $b_n(T)$ of $T$ satisfying $b^{-1}d_n\le b_n(T)\le bd_n$ for all $n$.

Key words and phrases: $B$-convex space, Bernstein numbers, Bernstein pair, uniformly complemented $\ell_2^n\,$, superstrictly singular operator.

MSC: 47B06, 47B10

Received: 02.08.2012

Language: English

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