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The Cauchy-Schwarz Inequality in Complex Normed Spaces - MaRDI portal

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The Cauchy-Schwarz Inequality in Complex Normed Spaces

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Publication:6282205

arXiv1701.06031MaRDI QIDQ6282205

Author name not available (Why is that?)

Publication date: 21 January 2017

Abstract: We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer. This also yields a new proof of the Cauchy-Schwarz inequality in complex inner product spaces, which does not rely on the linearity of the inner product. The proof depends only on the norm in the vector space. Further, we present some properties of the generalized product.





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