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Subjects
46-XX Functional analysis
46Cxx Inner product spaces and their generalizations, Hilbert spaces
46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)

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Displaying 1 – 3 of 3

The approximation of continuous linear functionals.

Sever Silvestru Dragomir (1991)

Extracta Mathematicae

The partial inner product space method: a quick overview.

Antoine, Jean-Pierre, Trapani, Camillo (2010)

Advances in Mathematical Physics

Two mappings related to semi-inner products and their applications in geometry of normed linear spaces

Sever Silvestru Dragomir, Jaromír J. Koliha (2000)

Applications of Mathematics

In this paper we introduce two mappings associated with the lower and upper semi-inner product ${(\cdot, \cdot)}_{i}$ and ${(\cdot, \cdot)}_{s}$ and with semi-inner products $[\cdot, \cdot]$ (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants.

Currently displaying 1 – 3 of 3

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