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On Edmunds-Triebel spaces. (English) Zbl 1198.46019
Summary: We consider the Edmunds-Triebel logarithmic spaces $A_\theta(\log A)_{b,q}$, produced by a Banach couple $\bar A=(A_0,A_1)$, as special cases of extrapolation spaces and get estimates of a measure of weak noncompactness of the unit balls of these spaces in terms of the measures of weak noncompactness of the unit balls of the spaces $A_0$ and $A_1$. We obtain also estimates of the $n$-th Jordan-von Neumann constant $C_n$ and the $n$-th James constant $J_n$ of the spaces $A_\theta(\log A)_{b,q}$ in terms of the corresponding constants of the spaces $A_0$ and $A_1$.

46B70Interpolation between normed linear spaces
46B20Geometry and structure of normed linear spaces
47H08Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
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