Results 1  10
of
346,627
The HahnBanach Theorem in Type Theory
, 1997
"... We give the basic deønitions for pointfree functional analysis and present constructive proofs of the Alaoglu and HahnBanach theorems in the setting of formal topology. 1 Introduction We present the basic concepts and deønitions needed in a pointfree approach to functional analysis via formal topol ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
We give the basic deønitions for pointfree functional analysis and present constructive proofs of the Alaoglu and HahnBanach theorems in the setting of formal topology. 1 Introduction We present the basic concepts and deønitions needed in a pointfree approach to functional analysis via formal
A GENERALIZATION OF THE HAHNBANACH THEOREM
"... Let K denote either the real field R of the complex field C. The HahnBanach theorem can be stated in the following form: THEOREM 0. Let E be a vector space over the field K, and q: Es>R a seminorm on E. Then, for each vector subspace EQ of E, and each linear ..."
Abstract
 Add to MetaCart
Let K denote either the real field R of the complex field C. The HahnBanach theorem can be stated in the following form: THEOREM 0. Let E be a vector space over the field K, and q: Es>R a seminorm on E. Then, for each vector subspace EQ of E, and each linear
HahnBanach theorems for κnormed spaces
, 2002
"... For a new class of topological vector spaces, namely κnormed spaces, an associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a κnorm, that is a distance function between a point and a Gδsubset. For it, analog ..."
Abstract
 Add to MetaCart
, analogs of the HahnBanach theorem are proved. 1 Introduction. Normable topological vector spaces play important role in functional analysis, but their class does not encompass all locally convex spaces. A new class of topological spaces, namely the class of κmetric topological spaces, was introduced
A HahnBanach Theorem for Integral Polynomials
"... We study the problem of extendibility of polynomials over Banach spaces: when can a polynomial defined over a Banach space be extended to a polynomial over any larger Banach space? To this end, we identify all spaces of polynomials as the topological duals of a space S spanned by evaluations, with H ..."
Abstract

Cited by 13 (10 self)
 Add to MetaCart
, with Hausdorff locally convex topologies. We prove that all integral polynomials over a Banach space are extendible. Finally, we study the AronBerner extension of integral polynomials, and give an equivalence for noncontainment of `1.
Hahn–Banach Operators: A Review
"... In this paper we review ongoing work on operators having normpreserving extensions to every overspace. We call them Hahn–Banach operators. KEY WORDS: Hahn–Banach operators. 1. ..."
Abstract
 Add to MetaCart
In this paper we review ongoing work on operators having normpreserving extensions to every overspace. We call them Hahn–Banach operators. KEY WORDS: Hahn–Banach operators. 1.
Uniform smoothness entails HahnBanach
 Quaestiones Mathematicae
"... Abstract. We show in set theory ZF (without the Axiom of Choice), that uniformly smooth normed spaces satisfy an effective and geometric form of the HahnBanach property. We also compare in ZF the two notions of Gâteaux differentiability and smoothness of a norm, and we obtain a new equivalent of th ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. We show in set theory ZF (without the Axiom of Choice), that uniformly smooth normed spaces satisfy an effective and geometric form of the HahnBanach property. We also compare in ZF the two notions of Gâteaux differentiability and smoothness of a norm, and we obtain a new equivalent
HahnBanach type theorems for Hilbert C*modules
 Internat. J. Math
"... Abstract. We show three HahnBanach type extension criteria for (sets of) bounded C*linear maps of Hilbert C*modules to the underlying C*algebras of coefficients. One criterion establishes an alternative description of the property of C*algebras to be monotone complete or additively complete. 1. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. We show three HahnBanach type extension criteria for (sets of) bounded C*linear maps of Hilbert C*modules to the underlying C*algebras of coefficients. One criterion establishes an alternative description of the property of C*algebras to be monotone complete or additively complete. 1.
A Direct Proof of the Localic HahnBanach Theorem
, 1999
"... Using the notion of entailment relation [Sco74] we give a direct proof of the localic version of HahnBanach's theorem. 1 Introduction There are several examples of topological spaces naturally associated to a mathematical structure: the spectrum (with Zariski topology) associated to a ring, ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Using the notion of entailment relation [Sco74] we give a direct proof of the localic version of HahnBanach's theorem. 1 Introduction There are several examples of topological spaces naturally associated to a mathematical structure: the spectrum (with Zariski topology) associated to a ring
HOW MUCH INCOMPUTABLE IS THE SEPARABLE HAHNBANACH THEOREM?
, 808
"... Abstract. We determine the computational complexity of the HahnBanach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable ..."
Abstract
 Add to MetaCart
Abstract. We determine the computational complexity of the HahnBanach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify
Results 1  10
of
346,627