相关论文: Hyper innerproduct spaces II
In this paper, we introduce the concept of inner product on weak hypervector spaces and prove some results about them.
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…
A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…
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)…
Well-known operations defined on a non-degenerate inner product vector space are extended to the case of a degenerate inner product. The main obstructions to the extension of these operations to the degenerate case are (1) the index…
We consider a tensor product of two spaces of holomorphic functions on a Hermitian symmetric space of tube type. Then generically this is decomposed into a direct sum of irreducible subrepresentations. In this manuscript, we construct the…
We give alternative proofs to certain results in the paper "Weak limits of almost invariant projections" by using ultraproducts of operators.
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…
We present natural (invariant) definite and indefinite scalar products on the N=1 superspace which turns out to carry an inherent Hilbert-Krein structure. We are motivated by supersymmetry in physics but prefer a general mathematical…
This note is devoted to establishing two-weight estimates for commutators of singular integrals. We combine multilinearity with product spaces. A new type of two-weight extrapolation result is used to yield the quasi-Banach range of…
If $\mathcal{H}$ denotes a Hilbert space of analytic functions on a region $\Omega \subseteq \mathbb{C}^d$, then the weak product is defined by $$\mathcal{H}\odot\mathcal{H}=\left\{h=\sum_{n=1}^\infty f_n g_n : \sum_{n=1}^\infty…
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…
We analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
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…
The field of real numbers being extended as a larger commutative field, we investigate the possibility of defining a scalar product for the distributions of finite discrete support. Then we focus on the most simple possible extension (which…
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product…
In this article the infinite product of bicomplex numbers is defined and the convergence and divergence of this product are discussed.
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few…