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Zbl 1198.46019
Nikolova, L.; Zachariades, T.
On Edmunds-Triebel spaces. (English)
[J] Banach J. Math. Anal. 4, No. 1, 146-158, electronic only (2010). ISSN 1735-8787/e

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 $A_1$.

MSC 2000:: *46B70 Interpolation between normed linear spaces
46B20 Geometry and structure of normed spaces
47H08

Keywords: Jordan-von Neumann constant; extrapolation spaces; logarithmic spaces; measure of non compactness; $n$-th James constant; Edmunds-Triebel logarithmic spaces

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Zentralblatt MATH Berlin [Germany]