On the complemented and uncomplemented subspaces in banach spaces

Fuctional analysis has risen at the beginning of the twentieth century. Currently, it occupies a distinguised postion among the contemporary Mathematics Sciences. It is not an exaggration to sate that funational analysis the revent trend in the mathimaticThe current thesis deals with one of the important theories of the functional analysis. It is defined as the isometric theory. It is a result of research conducted by a group of scholars. Banach is a leading scientist who published his book entitled to thThe current thesis is an extension to the work of those scholars. It focuses on one important and central question, which could be phrased as follows: when does Banach space become isomorphic to a Hilbert space? Many scholars have attempted that question.