All maximal commutative subalgebras occur in $L(X)$ uncountably many times

Restrictions of CP-Semigroups to Maximal Commutative Subalgebras

We give a necessary and sufficient criterion when a normal CP-map on a von Neumann algebra admits a restriction to a maximal commutative subalgebra. We apply this result to give a far reaching generalization of Rebolledo’s sufficient criterion for the Lindblad generator of a Markov semigroup on B(G). This work is supported by research funds of Italian MIUR (PRIN 2005). MS is supported by resear...

Spaces of Uncountably Many Dimensions*

Riemann in his Habilitations Schrift of 1854 suggested the notion of ^-dimensional space (where n is a natural number) as an extension of the notion of three-dimensional euclidean space. Hubert extended the notion still further by defining a space of a countably infinite number of dimensions. Fréchetf in 1908 defined two other spaces of countably many dimensions, which he called D„ and J3W. Tyc...

FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE RESIDUATED LATTICES

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

Dcpos of Commutative C*-subalgebras

Maximal Nonfinitely Generated Subalgebras

We show that “every countable algebra with a nonfinitely generated subalgebra has a maximal nonfinitely generated subalgebra” is provably equivalent to ’1-CA0 over RCA0.