Behrends, Ehrhard A generalization of the principle of local reflexivity. (English) Zbl 0609.46006 Rev. Roum. Math. Pures Appl. 31, 293-296 (1986). Our main result is the following generalization of the principle of local reflexivity: For every Banach space X, finite-dimensional subspaces \(E\subset X''\), \(G\subset X'\), \(H\subset L(X)\), and \(\epsilon >0\) there is an isomorphism T from \(F:=E+lin\{R''E| R\in H\}\) into X such that 1. \(\| T\|\| T^{-1}\| \leq 1+\epsilon\) 2. \(T|_{E\cap X}=Id|_{E\cap X}\) 3. \(x'(Tx'')=x''(x')\) for x”\(\in F\), x’\(\in G\) 4. \(\| (TR''-RT)|_ E\| \leq \epsilon \| R\|\) for \(R\in H\). Cited in 1 ReviewCited in 10 Documents MSC: 46B10 Duality and reflexivity in normed linear and Banach spaces 46B20 Geometry and structure of normed linear spaces Keywords:principle of local reflexivity PDFBibTeX XMLCite \textit{E. Behrends}, Rev. Roum. Math. Pures Appl. 31, 293--296 (1986; Zbl 0609.46006)