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In this paper are proved a few properties about convergent sequences into a real 2normed
space
( , , ) L and into a 2preHilbert space
( ,( ,  )) L , which are actually generalization of
appropriate properties of convergent sequences into a preHilbert space. Also, are given two
characterization of a 2Banach spaces. These characterization in fact are generalization of appropriate
results in Banach spaces.
2010 Mathematics Subject Classification: Primary 46B20; Secondary 46C05
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