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We provide for every 2 ≤ k ≤ n an n-dimensional Banach space E with a unique distance ellipsoid such that there are precisely k linearly independent contact points between and $B_{E}$ . The corresponding result holds for spaces with non-unique distance ellipsoids as well. We construct n-dimensional Banach spaces E such that one distance ellipsoid has precisely k linearly independent contact points and all other distance ellipsoids have less than k-1 such points.

Remarks concerning the paper "On a class of Hausdorff compacts and GSG Banach spaces"

Wolfgang Ruess, Charles Stegall (1985)

Studia Mathematica

Remarks on a theorem of S.N. Bernstein

G. Albinus (1970)

Studia Mathematica

Remarks on asymptotic centers and fixed points.

Kaewkhao, A., Sokhuma, K. (2010)

Abstract and Applied Analysis

Remarks on compact operators between interpolation spaces associated to polygons.

Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez (2006)

RACSAM

This note deals with interpolation methods defined by means of polygons. We show necessary and sufficient conditions for compactness of operators acting from a J-space into a K-space.

Remarks on continuous images of Radon-Nikodým compacta

Marián J. Fabián, Martin Heisler, Eva Matoušková (1998)

Commentationes Mathematicae Universitatis Carolinae

A family of compact spaces containing continuous images of Radon-Nikod’ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod’ym compact $K$ we prove: If $K$ is totally disconnected, then it is Radon-Nikod’ym compact. If $K$ is adequate, then it is even Eberlein compact.

Remarks on embeddable semigroups in groups and a generalization of some Cuthbert's results.

Latrach, Khalid, Dehici, Abdelkader (2003)

International Journal of Mathematics and Mathematical Sciences

Remarks on independent sequences and dimension in topological linear spaces.

Z. Lipecki (1998)

Collectanea Mathematica

Remarks on interpolation of bilinear operators by methods associated to polygons

P. Fernández-Martínez (2003)

Bollettino dell'Unione Matematica Italiana

We study interpolation of bilinear operators by the polygons methods. We prove an interpolation theorem of type $K \times K$ into $K$ spaces, and show the optimality of the precedings results.

Remarks on orthogonality preserving mappings in normed spaces and some stability problems.

Chmieliński, Jacek (2007)

Banach Journal of Mathematical Analysis [electronic only]

Remarks on remotal sets in vector valued function spaces.

Sababheh, M., Khalil, R. (2009)

The Journal of Nonlinear Sciences and its Applications

Remarks on rich subspaces of Banach spaces

Vladimir Kadets, Nigel Kalton, Dirk Werner (2003)

Studia Mathematica

We investigate rich subspaces of L₁ and deduce an interpolation property of Sidon sets. We also present examples of rich separable subspaces of nonseparable Banach spaces and we study the Daugavet property of tensor products.

Remarks on some properties in the geometric theory of Banach spaces

Wagdy Gomaa El-Sayed, Krzysztof Fraczek (1996)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to derive some relationships between the concepts of the property of strong $(α^{'})$ introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and Sȩkowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu.

Remarks on Strict Monotonicity and Surjectivity Properties of Duality Mappings Definied on Real Normed Linear Spaces.

Charles R. DePrima, W.V. Petryshyn (1971)

Mathematische Zeitschrift

Remarks on subdifferentials of convex functionals

Ho Duc Viet (1975)

Commentationes Mathematicae Universitatis Carolinae

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