engleski

Geometric constants for Banach spaces with absolute normalized norms which corresponding functions are comparable

In this paper we consider some geometric constants of ${; ; ; \bf C}; ; ; ^2$ equipped with an absolute normalized norm such as: the James constant $J(\|.\|_{; ; ; \psi}; ; ; )$, the von Neumann- -Jordan constant $C_{; ; ; NJ}; ; ; (\|.\|_{; ; ; \psi}; ; ; )$, the Gao constants $E(\|.\|_{; ; ; \psi}; ; ; )$ and $f(\|.\|_{; ; ; \psi}; ; ; )$, the Zb\u{; ; ; a}; ; ; ganu constant $C_{; ; ; Z}; ; ; (\|.\|_{; ; ; \psi}; ; ; )$ and constant $A_2(\|.\|_{; ; ; \psi}; ; ; )$. In particular we investigate relations involving these constants of the norms $\|.\|_{; ; ; \psi}; ; ; $ and $\|.\|_{; ; ; \psi_*}; ; ; $ where the convex functions $\psi$ and $ \psi_*$ are comparable. Also, we determine these constants when norm is a mean of two norms. Finally, these constants are calculated for some spaces such as the $X^p$ space, the Ces\`{; ; ; a}; ; ; ro sequence space etc.

absolute normalized norm; convex function; the James constant; the von Neumann-Jordan constant; Gao's constants

nije evidentirano