Bilipschitz mappings and strong weights.
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Semmes, Stephen (1992)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
M. S. Tomás (2005)
Bollettino dell'Unione Matematica Italiana
The study of circumcenters in different types of triangles in real normed spaces gives new characterizations of inner product spaces.
Arambašić, Ljiljana, Bakić, Damir, Rajić, Rajna (2010)
Banach Journal of Mathematical Analysis [electronic only]
Gervais Lavoie, Raphaël, Marchildon, Louis, Rochon, Dominic (2010)
Annals of Functional Analysis (AFA) [electronic only]
Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)
Mathematica Bohemica
Let be a complex Hilbert space, a positive operator with closed range in and the sub-algebra of of all -self-adjoint operators. Assume onto itself is a linear continuous map. This paper shows that if preserves -unitary operators such that then defined by is a homomorphism or an anti-homomorphism and for all , where and is the Moore-Penrose inverse of . A similar result is also true if preserves -quasi-unitary operators in both directions such that there exists an...
Aleksander Misiak, Alicja Ryż (2000)
Mathematica Bohemica
This paper is a continuation of investigations of -inner product spaces given in [five, six, seven] and an extension of results given in [three] to arbitrary natural . It concerns families of projections of a given linear space onto its -dimensional subspaces and shows that between these families and -inner products there exist interesting close relations.
Ambrozie, C.-G. (2005)
Portugaliae Mathematica. Nova Série
Chmieliński, Jacek (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Miličić, M. (1996)
Publications de l'Institut Mathématique. Nouvelle Série
Kürsten, K.-D., Wagner, E. (2000)
Zeitschrift für Analysis und ihre Anwendungen
Chang, Shihsen, Chen, Yuqing, Lee, Byung Soo (1997)
International Journal of Mathematics and Mathematical Sciences
João de Deus Marques (2000)
Czechoslovak Mathematical Journal
Let be a real linear space. A vectorial inner product is a mapping from into a real ordered vector space with the properties of a usual inner product. Here we consider to be a -regular Yosida space, that is a Dedekind complete Yosida space such that , where is the set of all hypermaximal bands in . In Theorem 2.1.1 we assert that any -regular Yosida space is Riesz isomorphic to the space of all bounded real-valued mappings on a certain set . Next we prove Bessel Inequality and Parseval...
Madjid Mirzavaziri, Mohammad Sal Moslehian (2006)
Kragujevac Journal of Mathematics
Rosa Fernández (1988)
Stochastica
Some generalized notions of James' orthogonality and orthogonality in the Pythagorean sense are defined and studied in the case of generalized normed spaces derived from generalized inner products.
Jaeseong Heo (2012)
Studia Mathematica
We consider positive definite kernels which are invariant under a multiplier and an action of a semigroup with involution, and construct the associated projective isometric representation on a Hilbert C*-module. We introduce the notion of C*-valued Hilbert-Schmidt kernels associated with two sequences and construct the corresponding reproducing Hilbert C*-module. We also discuss projective invariance of Hilbert-Schmidt kernels. We prove that the range of a convolution type operator associated with...
Chmieliński, Jacek (2007)
Banach Journal of Mathematical Analysis [electronic only]
P. M. Miličić (1971)
Matematički Vesnik
Sever Silvestru Dragomir (1991)
Extracta Mathematicae
Antoine, Jean-Pierre, Trapani, Camillo (2010)
Advances in Mathematical Physics
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 and and with semi-inner products (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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