1,940 research outputs found
The Daugavet property of -algebras, -triples, and of their isometric preduals
A Banach space is said to have the Daugavet property if every rank-one
operator satisfies . We give
geometric characterizations of this property in the settings of -algebras,
-triples and their isometric preduals. We also show that, in these
settings, the Daugavet property passes to ultrapowers, and thus, it is
equivalent to an stronger property called the uniform Daugavet property.Comment: To appear in J. Funct. Anal., final form, 19 page
Information completeness in Nelson algebras of rough sets induced by quasiorders
In this paper, we give an algebraic completeness theorem for constructive
logic with strong negation in terms of finite rough set-based Nelson algebras
determined by quasiorders. We show how for a quasiorder , its rough
set-based Nelson algebra can be obtained by applying the well-known
construction by Sendlewski. We prove that if the set of all -closed
elements, which may be viewed as the set of completely defined objects, is
cofinal, then the rough set-based Nelson algebra determined by a quasiorder
forms an effective lattice, that is, an algebraic model of the logic ,
which is characterised by a modal operator grasping the notion of "to be
classically valid". We present a necessary and sufficient condition under which
a Nelson algebra is isomorphic to a rough set-based effective lattice
determined by a quasiorder.Comment: 15 page
An asymptotic dimension for metric spaces, and the 0-th Novikov-Shubin invariant
A nonnegative number d_infinity, called asymptotic dimension, is associated
with any metric space. Such number detects the asymptotic properties of the
space (being zero on bounded metric spaces), fulfills the properties of a
dimension, and is invariant under rough isometries. It is then shown that for a
class of open manifolds with bounded geometry the asymptotic dimension
coincides with the 0-th Novikov-Shubin number alpha_0 defined previously
(math.OA/9802015, cf. also math.DG/0110294). Thus the dimensional
interpretation of alpha_0 given in the mentioned paper in the framework of
noncommutative geometry is established on metrics grounds. Since the asymptotic
dimension of a covering manifold coincides with the polynomial growth of its
covering group, the stated equality generalises to open manifolds a result by
Varopoulos.Comment: 17 pages, to appear on the Pacific Journal of Mathematics. This paper
roughly corresponds to the third section of the unpublished math.DG/980904
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