Bilipschitz mappings and strong weights.
Circumcenters in real normed spaces
The study of circumcenters in different types of triangles in real normed spaces gives new characterizations of inner product spaces.
Finite-dimensional Hilbert -modules.
Infinite-dimensional bicomplex Hilbert spaces.
Linear maps preserving -unitary operators
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...
-inner product spaces and projections
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.
On a completion of prehilbertian spaces.
On an -Birkhoff orthogonality.
On isomorphisms by orthogonality of a normed space and an inner product space.
On representations of partial *-algebras based on -weights.
On the semi-inner product in locally convex spaces.
On vectorial inner product spaces
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...
Orthogonal constant mappings in isosceles orthogonal spaces
Ortogonalidad en espacios normados generalizados.
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.
Projectively invariant Hilbert-Schmidt kernels and convolution type operators
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...
Remarks on orthogonality preserving mappings in normed spaces and some stability problems.
Sur le semi-product scalaire dans quelques espaces vectoriels normés
The approximation of continuous linear functionals.
The partial inner product space method: a quick overview.
Two mappings related to semi-inner products and their applications in geometry of normed linear spaces
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.