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Abstract
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 mathimatical thinking like what had happen with previous domain of variables in the mathimatic in seventh centeray which led to establishing the arithmetic of the calculus. After publishing the book of the greate of mathematician ‘Banch’ “ Theorie das operation linearies”, many thoughts and the language of functional analysis paved their way to various subjects of mathmatic and their application. Thus, it has, extermally difficult sometimes to separate between functional analysis and their applications.
The 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 theorie das oprations lineaires in 1932.
The 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. Their attempts were satisfactory and acceptable.