Results 1 
4 of
4
On Köthe sequence spaces and linear logic
 Mathematical Structures in Computer Science
, 2001
"... We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Kothe sequence spaces. In this setting, the spaces interpreting the exponential have a quite simple structure of commutative Hopf algebra. The ..."
Abstract

Cited by 26 (7 self)
 Add to MetaCart
We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Kothe sequence spaces. In this setting, the spaces interpreting the exponential have a quite simple structure of commutative Hopf algebra. The coKleisli category of this linear category is a cartesian closed category of entire mappings. This work provides a simple setting where typed calculus and dierential calculus can be combined; we give a few examples of computations. 1
Bounded and unitary elements in proC ∗algebras ∗
, 2005
"... A proC ∗algebra is a (projective) limit of C ∗algebras in the category of topological ∗algebras. From the perspective of noncommutative geometry, proC ∗algebras can be seen as noncommutative kspaces. An element of a proC ∗algebra is bounded if there is a uniform bound for the norm of its ..."
Abstract
 Add to MetaCart
A proC ∗algebra is a (projective) limit of C ∗algebras in the category of topological ∗algebras. From the perspective of noncommutative geometry, proC ∗algebras can be seen as noncommutative kspaces. An element of a proC ∗algebra is bounded if there is a uniform bound for the norm of its images under any continuous ∗homomorphism into a C ∗algebra. The ∗subalgebra consisting of the bounded elements turns out to be a C ∗algebra. In this paper, we investigate proC ∗algebras from a categorical point of view. We study the functor (−)b that assigns to a proC ∗algebra the C ∗algebra of its bounded elements, which is the dual of the StoneČechcompactification. We show that (−)b is a coreflector, and it preserves exact sequences. A generalization of the Gelfandduality for commutative unital proC ∗algebras is also presented. 1.
The egometry of the loop space and a . . .
, 2008
"... We describe a construction of fibrewise inner products on the cotangent bundle of the smooth free loop space of a Riemannian manifold. Using this inner product, we construct an operator over the loop space of a string manifold which is directly analogous to the Dirac operator of a spin ..."
Abstract
 Add to MetaCart
We describe a construction of fibrewise inner products on the cotangent bundle of the smooth free loop space of a Riemannian manifold. Using this inner product, we construct an operator over the loop space of a string manifold which is directly analogous to the Dirac operator of a spin
Mathematik und Naturwissenschaften
"... The present thesis approaches the loop space of a Riemannian 3manifold (M, 〈, 〉) from a geometric point of view. Loops are immersed circles represented by immersions γ: S 1 → M modulo reparametrizations. In this setup, the loop space M appears as the base of a principal bundle π: Imm(S 1, M) → Imm ..."
Abstract
 Add to MetaCart
The present thesis approaches the loop space of a Riemannian 3manifold (M, 〈, 〉) from a geometric point of view. Loops are immersed circles represented by immersions γ: S 1 → M modulo reparametrizations. In this setup, the loop space M appears as the base of a principal bundle π: Imm(S 1, M) → Imm(S 1, M)/Di (S 1) =: M. The tangent space at γ may be identi ed with the space Γ(⊥γ) of smooth sections of the loop's normal bundle. A ne connections on M are constructed. Firstly, the LeviCivita connection ∇LC belonging to the Kähler structure (J, 〈〈, 〉〉), where 〈〈, 〉 〉 denotes the L2 product of normal elds and the almost complex structure J is given by 90 ◦ left rotation in the normal bundle. Its curvature and topological properties of the distance function induced by 〈〈, 〉 〉 are analyzed. Secondly, a previously unknown complex linear connection ∇C on M is described, which depends only on the conformal class of (M, 〈, 〉). The introduction of the conformally invariant harmonic mean