Displaying similar documents to “On commutative approximate identities”

Commutative directoids with sectional involutions

Ivan Chajda (2007)

Discussiones Mathematicae - General Algebra and Applications

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The concept of a commutative directoid was introduced by J. Ježek and R. Quackenbush in 1990. We complete this algebra with involutions in its sections and show that it can be converted into a certain implication algebra. Asking several additional conditions, we show whether this directoid is sectionally complemented or whether the section is an NMV-algebra.

Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type

Thomas Meyer (1997)

Studia Mathematica

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Let ε ω ( I ) denote the space of all ω-ultradifferentiable functions of Roumieu type on an open interval I in ℝ. In the special case ω(t) = t we get the real-analytic functions on I. For μ ∈ ε ω ( I ) ' with s u p p ( μ ) = 0 one can define the convolution operator T μ : ε ω ( I ) → ε ω ( I ) , T μ ( f ) ( x ) : = ⟨ μ , f ( x - · ) ⟩ . We give a characterization of the surjectivity of T μ for quasianalytic classes ε ω ( I ) , where I = ℝ or I is an open, bounded interval in ℝ. This characterization is given in terms of the distribution of zeros of the Fourier Laplace transform μ ^ of μ.

The two-square lemma.

Temple H. Fay, Keith A. Hardie, Peter J. Hilton (1989)

Publicacions Matemàtiques

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A new proof is given of the connecting homomorphism.