Glasnik Matematicki, Vol. 37, No.1 (2002), 133-139.

ON REDUNDANCE OF ONE OF THE AXIOMS OF A GENERALIZED NORMED SPACE

Dijana Ilisevic

Department of Mathematics, University of Zagreb, Bijenicka 30, P.O.Box 335, 10002 Zagreb, Croatia
e-mail: ilisevic@math.hr

Abstract.   It is shown that one of the Zalar's axioms of a generalized normed space is redudant. More precisely, Jordan - von Neumann type theorem for a pre-Hilbert module is also valid if that axiom is omitted.

2000 Mathematics Subject Classification.   46K15, 46C15, 46H25.

Key words and phrases.   H*-algebra, Hilbert module, normed module, Jordan - von Neumann theorem.

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