Hanner inequalities

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The Hanner inequalities come from functional analysis and are inequalities for L p norms . They have some important consequences, including that the L p spaces are for uniformly convex spaces .

They are named after the Swedish mathematician Olof Hanner .


Be . If so , then



If so , then the inequality symbols are reversed, that is, becomes off .

Explanations of the inequalities

The second inequality is obtained from the first by substituting and . Because then the left side becomes too

and the right side is reshaped similarly.

For the norm is induced by a scalar product . In this case, the inequalities become equations and are equivalent to the parallelogram equation .

Individual evidence

  1. C. Schütt: functional analysis , page 73. Accessed June 24, 2020.