95,274 research outputs found
Ranges of bimodule projections and reflexivity
We develop a general framework for reflexivity in dual Banach spaces,
motivated by the question of when the weak* closed linear span of two reflexive
masa-bimodules is automatically reflexive. We establish an affirmative answer
to this question in a number of cases by examining two new classes of
masa-bimodules, defined in terms of ranges of masa-bimodule projections. We
give a number of corollaries of our results concerning operator and spectral
synthesis, and show that the classes of masa-bimodules we study are operator
synthetic if and only if they are strong operator Ditkin
Classical Mathematics for a Constructive World
Interactive theorem provers based on dependent type theory have the
flexibility to support both constructive and classical reasoning. Constructive
reasoning is supported natively by dependent type theory and classical
reasoning is typically supported by adding additional non-constructive axioms.
However, there is another perspective that views constructive logic as an
extension of classical logic. This paper will illustrate how classical
reasoning can be supported in a practical manner inside dependent type theory
without additional axioms. We will see several examples of how classical
results can be applied to constructive mathematics. Finally, we will see how to
extend this perspective from logic to mathematics by representing classical
function spaces using a weak value monad.Comment: v2: Final copy for publicatio
Reflexivity of the isometry group of some classical spaces
We investigate the reflexivity of the isometry group and the automorphism
group of some important metric linear spaces and algebras. The paper consists
of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of
measurable functions. 4. Hardy spaces. 5. Banach algebras of holomorphic
functions. 6. Frechet algebras of holomorphic functions. 7. Spaces of
continuous functions.Comment: 18 pages. To appear in Rev. Mat. Iberoa
A Nonmonotonic Sequent Calculus for Inferentialist Expressivists
I am presenting a sequent calculus that extends a nonmonotonic consequence relation over an atomic language to a logically complex language. The system is in line with two guiding philosophical ideas: (i) logical inferentialism and (ii) logical expressivism. The extension defined by the sequent rules is conservative. The conditional tracks the consequence relation and negation tracks incoherence. Besides the ordinary propositional connectives, the sequent calculus introduces a new kind of modal operator that marks implications that hold monotonically. Transitivity fails, but for good reasons. Intuitionism and classical logic can easily be recovered from the system
When Structural Principles Hold Merely Locally
In substructural logics, structural principles may hold in some fragments of a consequence relation without holding globally. I look at this phenomenon in my preferred substructural logic, in which Weakening and Cut fail but which is supra-intuitionistic. I introduce object language operators that keep track of the admissibility of Weakening and of intuitionistic implications. I end with some ideas about local transitivity
Bourdieu and the dead end of reflexivity: on the impossible task of locating the subject
This article examines recent attempts by IR scholars to flesh out a reflexive approach inspired by the work of Pierre Bourdieu. The French sociologist pioneered the idea of turning the tools of sociology onto oneself in order to apply the same grid of social analysis to the object and subject of scholarship. This represents the culmination of a long tradition of seeking to understand from where one speaks and grasp our subjective biases through reflexive means. But as I argue Bourdieu – like most reflexive scholars – largely overestimated his ability to grasp his own subject position. For he assumed he could be objective about the very thing he had the least reasons to be objective about: himself. Instead of bending over backwards in this way and directly take the subject into account, I then propose to rearticulate the problematic of reflexivity by going back to a more classic concern with the question of alienation. Through a detailed critique of Bourdieu's reflexive approach and the ways in which it was received in IR, I set out a series of principles to reconfigure the agenda of reflexivity and offer a platform for a proper methodological alternative to positivism
Uniformly convex metric spaces
In this paper the theory of uniformly convex metric spaces is developed.
These spaces exhibit a generalized convexity of the metric from a fixed point.
Using a (nearly) uniform convexity property a simple proof of reflexivity is
presented and a weak topology of such spaces is analyzed. This topology called
co-convex topology agrees with the usualy weak topology in Banach spaces. An
example of a -spaces with weak topology which is not Hausdorff is
given. This answers questions raised by Monod 2006, Kirk and Panyanak 2008 and
Esp\'inola and Fern\'andez-Le\'on 2009.
In the end existence and uniqueness of generalized barycenters is shown and a
Banach-Saks property is proved.Comment: 23 page
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