Triangle Congruence Characterizations of Inner Product Spaces

Abstract

I n a number of instances, the notion of angle in a normed linear space has been used to derive characterizations of real inner product spaces. Particular examples of such characterizations are those of MARTIN and VALENTINE [6], VALENTINE [a], VALENTINE and WAYMENT [9]. and SUNDARESAN [7]. (For a summary of these and other results see AMIR [l]). The present authors, in [3] and [4], defined an angle, A ( -, -) between nonzero elements of a real normed linear space by A(z, y) = spaces based on properties of angles and bisectors in euclidean plane geometry. I n the present paper, the authors present another sequence of characterizations based on euclidean triangle congruence properties.

A characterization of inner product spaces

“…inner product space; Euler-Lagrange identity; Day's condition; normed space; characterization; operator. characterizations of inner product spaces introduced by many mathematicians some of which are [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”