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Displaying 21 – 33 of 33

The $n$ -dual space of the space of $p$ -summable sequences

Yosafat E. P. Pangalela, Hendra Gunawan (2013)

Mathematica Bohemica

In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an $n$ -normed space, we are interested in bounded multilinear $n$ -functionals and $n$ -dual spaces. The concept of bounded multilinear $n$ -functionals on an $n$ -normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear $n$ -functionals, introduce the concept of $n$ -dual spaces, and...

The ordering of experimental designs. A Hilbert space approach

Andrej Pázman (1974)

Kybernetika

The Orthogonal Projection and the Riesz Representation Theorem

Keiko Narita, Noboru Endou, Yasunari Shidama (2015)

Formalized Mathematics

In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals...

The partial inner product space method: a quick overview.

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

Advances in Mathematical Physics

The Small Ball Theorem for Hilbert Spaces.

Jens Peter Reuss Christensen (1978)

Mathematische Annalen

The space of all bounded operators on Hilbert space does not have the approximation property

A. Szankowski (1978/1979)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Topologías admisibles en espacios con producto interior descomponible.

Robert Fuster Capilla (1985)

Stochastica

In this note we determine the class of indefinite and decomposable inner product spaces in which the natural topology is admissible and we prove the continuity of orthogonal projections in these spaces.

Topological groups and convex sets homeomorphic to non-separable Hilbert spaces

Taras Banakh, Igor Zarichnyy (2008)

Open Mathematics

Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover $𝒰$ of X there is a sequence of maps (f n: X → X)nεgw such that each f n is $𝒰$ -near to the identity map of X and the family f n(X)n∈ω is locally finite...

Total Minimality of the Unitary Groups.

L. Stojanov (1984)

Mathematische Zeitschrift

Transformations canoniques linéaires dans les espaces de Hilbert

Michel Marias (1977/1978)

Séminaire Paul Krée

Transitivity of the norm on Banach spaces.

Julio Becerra Guerrero, A. Rodríguez-Palacios (2002)

Extracta Mathematicae

Two examples of non-separable metrizable spaces

R. Pol (1975)

Colloquium Mathematicae

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.

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