<![CDATA[If X is a Gelfand-Phillips space, then every sequence which is equivalent to contains an infinite subsequence such that is complemented in X. is the space of all sequences such that as . The norm is It is known that if every limited set of X is relatively weakly compact, then every copy of in X contains a subspace still isomorphic to which is complemented in X. A Banach space is said to have the Gelfand-Phillips property if every limited subset is relatively norm compact. The question whether if a Fre’chet space does not contain implies it can admit or have the Gelfand-Phillips property is still open. The purpose of this study was to establish the conditions for which a Fre’chet Space can admit the Gelfand-Phillips property without . We investigated the conditions on which a Fre’chet space not containing admits the Gelfand-Phillips property. The methodology involved the use of literature study related to Fre’chet spaces and Gelfand-Phillips property. The conditions which imply that a Fre’chet space has the Gelfand-Phillips property in spite of it not containing were given. It was established that if a Fre’chet space has a compact subspace , then it admits the Gelfand-Phillips property even if it doesn’t contain . The results in this study have a momentous contribution in the field of Mathematical Analysis.]]>
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