A direct approach to co-universal algebras associated to directed graphs.
A direct sum is holomorphically bornological with the topology induced by a cartesian product
A direct sum representation
A discontinuous function does not operate on the real part of a function algebra
A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle.
A discrete integral representation for polynomials of fixed maximal degree and their universal Korovkin closure.
A Discretized Approach to W. T. Gowers' Game
We give an alternative proof of W. T. Gowers' theorem on block bases by reducing it to a discrete analogue on specific countable nets. We also give a Ramsey type result on k-tuples of block sequences in a normed linear space with a Schauder basis.
A disjointness property of sequences in
A disjointness type property of conditional expectation operators
We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.
A distribution Hardy transformation.
A Distribution - Theoretic Proof of Kirillov's Character Formula for Nilpotent Lie Groups.
A distributional representation of strip analytic functions.
A distributional summation formula of Euler-MacLaurin type in two variables.
A domination theorem for function algebras
A double commutant theorem for purely large C*-subalgebras of real rank zero corona algebras
Let 𝓐 be a unital separable simple nuclear C*-algebra such that ℳ (𝓐 ⊗ 𝓚) has real rank zero. Suppose that ℂ is a separable simple liftable and purely large unital C*-subalgebra of ℳ (𝓐 ⊗ 𝓚)/ (𝓐 ⊗ 𝓚). Then the relative double commutant of ℂ in ℳ (𝓐 ⊗ 𝓚)/(𝓐 ⊗ 𝓚) is equal to ℂ.
A dual property to uniform monotonicity in Banach lattices.
For Banach lattices X with strictly or uniformly monotone lattice norm dual, properties (o)-smoothness and (o)-uniform smoothness are introduced. Lindenstrauss type duality formulas are proved and duality theorems are derived. It is observed that (o)-uniformly smooth Banach lattices X are order dense in X**. An application to an optimization theorem is given.
A Duality Between Hilbert Modules And Fields Of Hilbert Spaces.
A Duality Theorem for Locally Convex Tensor Products.
-algebras and topology of mapping tori
The paper studies applications of -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension , and . In conclusion, we consider two numerical examples illustrating our main results.
A factorization theorem for square area-integrable analytic functions.