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New variants of Khintchine's inequality.

Ioan Serb — 2001

Collectanea Mathematica

Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.

Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces

Ioan Şerb — 1999

Commentationes Mathematicae Universitatis Carolinae

Some characterizations of inner product spaces in terms of Birkhoff orthogonality are given. In this connection we define the rectangular modulus μ X of the normed space X . The values of the rectangular modulus at some noteworthy points are well-known constants of X . Characterizations (involving μ X ) of inner product spaces of dimension ≥ 2 , respectively ≥ 3 , are given and the behaviour of μ X is studied.

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