Numerical Index & Quotient Lifting Property

This thesis is divided in two main parts. One part deals with the numerical index. The computation of numerical index of real two dimensional $\ell_p$ (i.e, $n(\ell_p^2)$) is the most important step in computation of the numerical index of $L_p$-spaces. It has been been shown that the numerical index real $\ell_p^2$ $(