This is an English edition of Dixmier's book, which is the first systematic exposition of the
algebraic approach to representations of Lie groups via representations of (or modules over) …

This book is about monotone complete C-algebras, their properties, and the new
classification theory (using spectroid invariants and a classification semigroup). A basic …

A complete characterization of those compact Hausdorff spaces is given such that for every
n, each normal element in the algebra C (X)⊗ M n of continuous functions from X to M n can …

Given a unital $ C^* $-subalgebra $\mathcal A\subseteq B (\mathcal H), $ we study the set of
all possible images of the injective envelope $ I (\mathcal A) $ of $\mathcal A $ that are …

Loomis–Sikorski representation of monotone -complete effect algebras Page 1 Fuzzy Sets
and Systems 157 (2006) 683–690 www.elsevier.com/locate/fss Loomis–Sikorski …

Let A be a separable C*-algebra and let Mloc (A) be the local multiplier algebra of A. It is
shown that every minimal closed prime ideal of Mloc (A) is primitive. If Prim (A) has a dense …

Using recent results on a generalized form of the Loomis–Sikorski theorem [A. Dvurečenskij,
Loomis–Sikorski theorem for σ-complete MV-algebras and ℓ-groups, J. Austral. Math. Soc …

We give a classification of “small” monotone complete C*-algebras by order properties. We
construct a corresponding semigroup. This classification filters out von Neumann algebras; …

Let m be a bounded, real valued measure on a field of sets. Then, by the Yosida-Hewitt
theorem, m has a unique decomposition into the sum of a countably additive and a singular …

Let B be a unital monotone σ-complete C*-algebra, X a Banach space and (T n)(n= 1, 2,…) a
sequence of weakly compact operators from B to X. Our key theorem implies that if lim T np …