92 research outputs found
Notes on divisible MV-algebras
In these notes we study the class of divisible MV-algebras inside the
algebraic hierarchy of MV-algebras with product. We connect divisible
MV-algebras with -vector lattices, we present the divisible hull as
a categorical adjunction and we prove a duality between finitely presented
algebras and rational polyhedra
Characteristic functions and joint invariant subspaces
Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that
T is a completely non-coisometric row contraction. We establish the existence
of a "one-to-one" correspondence between the joint invariant subspaces under
T_1,..., T_n, and the regular factorizations of the characteristic function
associated with T. In particular, we prove that there is a non-trivial joint
invariant subspace under the operators T_1,..., T_n, if and only if there is a
non-trivial regular factorization of the characteristic function. We also
provide a functional model for the joint invariant subspaces in terms of the
regular factorizations of the characteristic function, and prove the existence
of joint invariant subspaces for certain classes of n-tuples of operators.
We obtain criterions for joint similarity of n-tuples of operators to Cuntz
row isometries. In particular, we prove that a completely non-coisometric row
contraction T is jointly similar to a Cuntz row isometry if and only if the
characteristic function of T is an invertible multi-analytic operator.Comment: 35 page
An analysis of the logic of Riesz Spaces with strong unit
We study \L ukasiewicz logic enriched with a scalar multiplication with
scalars taken in . Its algebraic models, called {\em Riesz MV-algebras},
are, up to isomorphism, unit intervals of Riesz spaces with a strong unit
endowed with an appropriate structure. When only rational scalars are
considered, one gets the class of {\em DMV-algebras} and a corresponding
logical system. Our research follows two objectives. The first one is to deepen
the connections between functional analysis and the logic of Riesz MV-algebras.
The second one is to study the finitely presented MV-algebras, DMV-algebras and
Riesz MV-algebras, connecting them from logical, algebraic and geometric
perspective
Fuzzy approach for CNOT gate in quantum computation with mixed states
In the framework of quantum computation with mixed states, a fuzzy
representation of CNOT gate is introduced. In this representation, the
incidence of non-factorizability is specially investigated.Comment: 14 pages, 2 figure
Lukasiewicz logic and Riesz spaces
We initiate a deep study of {\em Riesz MV-algebras} which are MV-algebras
endowed with a scalar multiplication with scalars from . Extending
Mundici's equivalence between MV-algebras and -groups, we prove that
Riesz MV-algebras are categorically equivalent with unit intervals in Riesz
spaces with strong unit. Moreover, the subclass of norm-complete Riesz
MV-algebras is equivalent with the class of commutative unital C-algebras.
The propositional calculus that has Riesz MV-algebras as
models is a conservative extension of \L ukasiewicz -valued
propositional calculus and it is complete with respect to evaluations in the
standard model . We prove a normal form theorem for this logic,
extending McNaughton theorem for \L ukasiewicz logic. We define the notions of
quasi-linear combination and quasi-linear span for formulas in and we relate them with the analogue of de Finetti's coherence
criterion for .Comment: To appear in Soft Computin
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