Results 11 to 20 of about 112 (106)

Unique Hahn-Banach extensions and Korovkin’s theorem [PDF]

Proceedings of the American Mathematical Society, 1975
This paper characterizes in terms of weak topologies those bounded linear functionals on a subspace which have unique Hahn-Banach extensions to the whole linear normed space. The relationship to the Choquet boundary is discussed, and a Korovkin type theorem is obtained.
openaire   +2 more sources

A Version of the Hahn-Banach Theorem for R-Vector Spaces [PDF]

Sahand Communications in Mathematical Analysis
Recently, $R$-metric spaces have been introduced to generalized metric spaces. This extension is based on the construction of a new universe with interesting properties.
Azadeh Alijani, Zohreh Heydarpour, Maryam Naderi Parizi   +2 more
doaj   +1 more source

On the extension of linear operators

International Journal of Mathematics and Mathematical Sciences, 2001
It is well known that the Hahn-Banach theorem, that is, the extension theorem for bounded linear functionals, is not true in general for bounded linear operators. A characterization of spaces for which it is true was published by Kakutani in 1940.
John J. Saccoman
doaj   +1 more source

Hahn-Banach type extension theorems on p-operator spaces [PDF]

Operators and Matrices, 2015
Let $V\subseteq W$ be two operator spaces. Arveson-Wittstock-Hahn-Banach theorem asserts that every completely contractive map $φ:V\to \mathcal{B}(H)$ has a completely contractive extension $\tildeφ:W\to \mathcal{B}(H)$, where $\mathcal{B}(H)$ denotes the space of all bounded operators from a Hilbert space $H$ to itself.
openaire   +2 more sources

Risk Measure Duality Without Structure

Mathematical Finance, EarlyView.
ABSTRACT We study risk measures on vector spaces of random variables which a priori have little structure, such as spaces lacking law invariance or a lattice structure. Ensuring the existence of a tractable dual representation (one which does not contain non‐sigma‐additive measures) is one of the main problems in risk measure theory, and we address it ...
Vasily Melnikov
wiley   +1 more source

Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson, Janne Nurminen, Mikko Salo   +2 more
wiley   +1 more source

On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces

Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 15358-15384, 15 September 2026.
ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
wiley   +1 more source

Some extensions of a dual of the Hahn-Banach Theorem, with applications to separation and Helly type theorems [PDF]

Bulletin of the Australian Mathematical Society, 1976
In previous papers we have proved that if G is a ω*-closed subspace of the conjugate space B* of a normed linear space B, then every b ∈ B can be extended within B, from G to the whole B*, with an arbitrarily small increase of the norm. Here we give some extensions of this result to the case when B* is replaced by a normed linear space E and B by any ...
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Amenability Constants for Unconditional Sums of Banach Algebras

Mathematische Nachrichten, Volume 299, Issue 9, Page 2472-2494, September 2026.
ABSTRACT We study Johnson amenability for unconditional direct sums of Banach algebras. Given a family (Ai)i∈I$(A_i)_{i\in I}$ of Banach algebras and a Banach sequence lattice E$E$ on I$I$, the E$E$‐sum ⨁i∈IAiE${\bigl (\bigoplus _{i\in I} A_i\bigr)}_{\!E}$ carries a natural Banach algebra structure via coordinatewise multiplication.
Tomasz Kania, Jerzy Ka̧kol
wiley   +1 more source

Null projections and noncommutative function theory in operator algebras

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract We study projections in the bidual of a C∗$\mathrm{C}^*$‐algebra B$B$ that are null with respect to a subalgebra A$A$, that is, projections p∈B∗∗$p\in B^{**}$ satisfying |φ|(p)=0$|\varphi |(p)=0$ for every φ∈B∗$\varphi \in B^*$ annihilating A$A$. In the separable case, A$A$‐null projections are precisely the peak projections in the bidual of A$
David P. Blecher, Raphaël Clouâtre
wiley   +1 more source