2,278 research outputs found
State morphism MV-algebras
We present a complete characterization of subdirectly irreducible MV-algebras
with internal states (SMV-algebras). This allows us to classify subdirectly
irreducible state morphism MV-algebras (SMMV-algebras) and describe single
generators of the variety of SMMV-algebras, and show that we have a continuum
of varieties of SMMV-algebras
Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
We study Archimedean atomic lattice effect algebras whose set of sharp
elements is a complete lattice. We show properties of centers, compatibility
centers and central atoms of such lattice effect algebras. Moreover, we prove
that if such effect algebra is separable and modular then there exists a
faithful state on . Further, if an atomic lattice effect algebra is densely
embeddable into a complete lattice effect algebra and the
compatiblity center of is not a Boolean algebra then there exists an
-continuous subadditive state on
Multipliers of embedded discs
We consider a number of examples of multiplier algebras on Hilbert spaces
associated to discs embedded into a complex ball in order to examine the
isomorphism problem for multiplier algebras on complete Nevanlinna-Pick
reproducing kernel Hilbert spaces. In particular, we exhibit uncountably many
discs in the ball of which are multiplier biholomorphic but have
non-isomorphic multiplier algebras. We also show that there are closed discs in
the ball of which are varieties, and examine their multiplier
algebras. In finite balls, we provide a counterpoint to a result of Alpay,
Putinar and Vinnikov by providing a proper rational biholomorphism of the disc
onto a variety in such that the multiplier algebra is not all
of . We also show that the transversality property, which is one
of their hypotheses, is a consequence of the smoothness that they require.Comment: 34 pages; the earlier version relied on a result of Davidson and
Pitts that the fibre of the maximal ideal space of the multiplier algebra
over a point in the open ball consists only of point evaluation. This result
fails for , and has necessitated some changes; to appear in
Complex Analysis and Operator Theor
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