Tangent segments in Minkowski planes.
The Bilinear Field of Values.
The determination of the spectral multiplicity of a stochastic process by RKHS method
The distance from a point to a cone in a Hilbert space.
The domain of attraction of a non-Gaussian stable distribution in a Hilbert space
The domain of attraction of a normal distribution in a Hilbert space
The general form of local bilinear functions
The scalar product of the FEM basis functions with non-intersecting supports vanishes. This property is generalized and the concept of local bilinear functional in a Hilbert space is introduced. The general form of such functionals in the spaces and is given.
The hypo-Euclidean norm of an -tuple of vectors in inner product spaces and applications.
The inclusion theorem for multiple summing operators
We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.
The laplacian and the Dirac operator in infinitely many variables
The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces
We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.
The mapping in normed linear spaces with applications to inequalities in analysis.
The multiplication functions of Kučera
The -dual space of the space of -summable sequences
In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an -normed space, we are interested in bounded multilinear -functionals and -dual spaces. The concept of bounded multilinear -functionals on an -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 -functionals, introduce the concept of -dual spaces, and...
The Small Ball Theorem for Hilbert Spaces.
The space of all bounded operators on Hilbert space does not have the approximation property
Transformations canoniques linéaires dans les espaces de Hilbert
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.