Affine semigroups and second duals.
Affine ultraregular generalized functions
Algebras of ultradifferentiable generalized functions satisfying some regularity assumptions are introduced. We give a microlocal analysis within these algebras related to the affine regularity type and the ultradifferentiability property. As a particular case we obtain new algebras of Gevrey generalized functions.
Algebra Involutions on the Bidual of a Banach Algebra.
Algebra isomorphisms between standard operator algebras
If X and Y are Banach spaces, then subalgebras ⊂ B(X) and ⊂ B(Y), not necessarily unital nor complete, are called standard operator algebras if they contain all finite rank operators on X and Y respectively. The peripheral spectrum of A ∈ is the set of spectral values of A of maximum modulus, and a map φ: → is called peripherally-multiplicative if it satisfies the equation for all A,B ∈ . We show that any peripherally-multiplicative and surjective map φ: → , neither assumed to be linear nor...
Algebra of multipliers on the space of real analytic functions of one variable
We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex. In particular, we show that Taylor multiplier sequences cease to be so after most permutations.
Algebra of observables and quantum logic
Algebrability of the set of non-convergent Fourier series
We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.
Algebraic and essentially algebraic composition operators on C(X).
Algebraic and topological properties of some sets in ℓ₁
For a sequence x ∈ ℓ₁∖c₀₀, one can consider the set E(x) of all subsums of the series . Guthrie and Nymann proved that E(x) is one of the following types of sets: () a finite union of closed intervals; () homeomorphic to the Cantor set; homeomorphic to the set T of subsums of where b(2n-1) = 3/4ⁿ and b(2n) = 2/4ⁿ. Denote by ℐ, and the sets of all sequences x ∈ ℓ₁∖c₀₀ such that E(x) has the property (ℐ), () and ( ), respectively. We show that ℐ and are strongly -algebrable and is -lineable. We...
Algebraic foundation of some distribution algebras
Algebraic generation of B(X) by two subalgebras with square zero
Algebraic genericity of strict-order integrability
We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and...
Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras
It is shown that every algebraic isomorphism between standard subalgebras of 𝒥-subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of 𝒥-subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a 𝒥-subspace lattice algebra can be written as a finite sum of rank one operators each belonging to that algebra. As an additional result, a multiplicative bijection of a 𝒥-subspace lattice algebra onto an arbitrary...
Algebraic -theory of Fredholm modules and -theory.
Algebraic properties of the 3-state vector Potts model
Algebraic quantum field theory and noncommutative moment problems. I
Algebraic quantum field theory and noncommutative moment problems. II
Algebraic reflexivity of C(X,E) and Cambern's theorem
The algebraic and topological reflexivity of C(X) and C(X,E) are investigated by using representations for the into isometries due to Holsztyński and Cambern.
Algebraic theory of Atkinson operators
Algebraic topology foundations of supersymmetry and symmetry breaking in quantum field theory and quantum gravity: a review.