arXiv subjects

Volker Wilhelm Thürey

Publications and source records attributed to Volker Wilhelm Thürey.

2 recordsLinked to original sources

arXiv2017

The Cauchy-Schwarz Inequality in Complex Normed Spaces

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.

math.FA↗

arXiv2012

Angles and a Classification of Normed Spaces

We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the special case of real inner product spaces. With these different angles we achieve a classification of normed spaces, and we obtain a characterization of inner product spaces. Finally we consider this construction also for a generalization of normed spaces, i.e. for spaces which may have a non-convex unit ball.

math.FA↗