Spectral resolutions for $σ$-complete lattice effect algebras

Rok, strany: 2006, 555 - 571

Recent results of the author about the existence of spectral measures for elements of $σ$-MV-algebras are applied to $σ$-complete lattice ordered effect algebras. It is shown that every element of a $σ$-complete lattice ordered effect algebra $E$ admits a spectral measure that does not depend on the block to which the element belongs, and every element is uniquely defined by its spectral measure. Further, every $σ$-additive state defined on the orthomodular $σ$-lattice of sharp elements $Sh(E)$ uniquely extends to a $σ$-additive state on the whole effect algebra, and pure states extend to pure states. To every element $a$ in $E$, there is the smallest sharp element dominating it, and this sharply dominating element is contained in every block to which $a$ belongs. Finally, it is shown that an effect-algebra commutator of two elements is sharply dominated by the commutator of their corresponding spectral measures, considered as real observables on $Sh(E)$.

ISO 690:

Pulmannová, S. 2006. Spectral resolutions for $σ$-complete lattice effect algebras. In Mathematica Slovaca, vol. 56, no.5, pp. 555-571. 0139-9918.

APA:

Pulmannová, S. (2006). Spectral resolutions for $σ$-complete lattice effect algebras. Mathematica Slovaca, 56(5), 555-571. 0139-9918.