Related papers: Hyperinner product spaces

In this paper, we extend the definition of hyperinner product defined on weak hypervector spaces with a hyperoperation scalar product to weak hypervector spaces with the hyperoperations sum and scalar products.

The main purpose of this paper is to generalize and develop a few basic properties of the innerproduct space on a hypervector space. On this hypervector space we define the norm. Also we establish a important relation between normed…

In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…

Some new Gruss type inequalities in inner product spaces and applications for integrals are given.

We present the basic concepts of tensor products of vector spaces, emphasizing linear algebraic and combinatorial techniques as needed for applied areas of research. The topics include (1) Introduction; (2) Basic multilinear algebra; (3)…

In this article we study a generalization of the n-inner product which we name weak n-inner product. As particular case we consider the n-iterated 2-inner product and we give its representation in terms of the standard k-inner products, k<=…

It is shown that inner functions in weak Besov spaces are precisely the exponential Blaschke products.

In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…

We give alternative proofs to certain results in the paper "Weak limits of almost invariant projections" by using ultraproducts of operators.

Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper.The results obtained here complement the recent work of the references.

We give a formula for the inner product of forms on a Hermitian vector space in terms of linear combinations of iterates of the adjoint of the Lefschetz operator. As an application, we reprove the Kobayashi-Lubke inequality for…

We discuss extensions of an inner product from a vector space to its full antidual. None of these extensions is weakly continuous, but partial extensions recapture some familiar structure including the Hilbert space completion and the…

The purpose of this survey is to give a comprehensive introduction to some classes of classical and recent analytic inequalities in Inner Product Spaces.

New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.

Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.

The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this…

A new inequality between angles in inner product spaces is formulated and proved. It leads directly to a concise statement and proof of the generalized Wielandt inequality, including a simple description of all cases of equality. As a…

It is proved that exponential Blaschke products are the inner functions whose derivative is in the weak Hardy space. Exponential Blaschke products are described in terms of their logarithmic means and also in terms of the behavior of the…

In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a uniformly…

This article is a follow-up to arXiv:2304.04373. We establish necessary and sufficient conditions for weighted Orlicz-Poincar\'e inequalities in product spaces. These results follow the work of Chua and Wheeden, who established similar…