Search results for "vector space"

Automatic continuity of generalized local linear operators

1980

In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.

Holomorphically ultrabornological spaces and holomorphic inductive limits

1987

Abstract The holomorphically ultrabornological spaces are introduced. Their relation with other holomorphically significant classes of locally convex spaces is established and separating examples are given. Some apparently new properties of holomorphically barrelled spaces are included and holomorphically ultrabornological spaces are utilized in a problem posed by Nachbin.

*-Representations, seminorms and structure properties of normed quasi*-algebras

2008

The class of -representations of a normed quasi -algebra (X;A0) is in- vestigated, mainly for its relationship with the structure of (X;A0). The starting point of this analysis is the construction of GNS-like -representations of a quasi -algebra (X;A0) dened by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms denes some seminorms (in some cases, C -seminorms) that provide useful information on the structure of (X;A0) and on the continuity properties of its -representations. 1. Introduction. A quasi -algebra is a couple (X;A0), where X is a vector space with involution , A0 is a -algebra and a vector subspace of X, and X is an A0-bimodule who…

Operators in Rigged Hilbert spaces: some spectral properties

2014

A notion of resolvent set for an operator acting in a rigged Hilbert space $\D \subset \H\subset \D^\times$ is proposed. This set depends on a family of intermediate locally convex spaces living between $\D$ and $\D^\times$, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.

The Action of the Symplectic Group Associated with a Quadratic Extension of Fields

1999

Abstract Given a quadratic extension L/K of fields and a regular alternating space (V, f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group SpL(V, f) in the set of K-subspaces of V.

On the stability of the Bohl — Brouwer — Schauder Theorem

1996

Transformations by diagonal matrices in a normed space

1962

Sets of Efficiency in a Normed Space and Inner Product

1987

In a normed space X the distances to the points of a given set A being considered as the objective functions of a multicriteria optimization problem, we define four sets of efficiency (efficient, strictly efficient, weakly efficient and properly efficient points). Instead of studying properties of the sets of efficiency according to properties of the norm, we investigate an inverse problem: deduce properties of the norm of X from properties of the sets of efficiency, valid for every finite subset A of X.

Polynomial identities for the Jordan algebra of a degenerate symmetric bilinear form

2013

Let J(n) be the Jordan algebra of a degenerate symmetric bilinear form. In the first section we classify all possible G-gradings on J(n) where G is any group, while in the second part we restrict our attention to a degenerate symmetric bilinear form of rank n - 1, where n is the dimension of the vector space V defining J(n). We prove that in this case the algebra J(n) is PI-equivalent to the Jordan algebra of a nondegenerate bilinear form.

On i-topological spaces: generalization of the concept of a topological space via ideals

2006

[EN] The aim of this paper is to generalize the structure of a topological space, preserving its certain topological properties. The main idea is to consider the union and intersection of sets modulo “small” sets which are defined via ideals. Developing the concept of an i-topological space and studying structures with compatible ideals, we are concerned to clarify the necessary and sufficient conditions for a new space to be homeomorphic, in some certain sense, to a topological space.