4,932 research outputs found
Maximal C*-algebras of quotients and injective envelopes of C*-algebras
A new C*-enlargement of a C*-algebra nested between the local multiplier
algebra of and its injective envelope is
introduced. Various aspects of this maximal C*-algebra of quotients,
, are studied, notably in the setting of AW*-algebras. As a
by-product we obtain a new example of a type I C*-algebra such that
.Comment: 37 page
Relative double commutants in coronas of separable C*-algebras
We prove a double commutant theorem for separable subalgebras of a wide class
of corona C*-algebras, largely resolving a problem posed by Pedersen. Double
commutant theorems originated with von Neumann, whose seminal result evolved
into an entire field now called von Neumann algebra theory. Voiculescu later
proved a C*-algebraic double commutant theorem for subalgebras of the Calkin
algebra. We prove a similar result for subalgebras of a much more general class
of so-called corona C*-algebras
Locally quasi-nilpotent elementary operators
Let be a unital dense algebra of linear mappings on a complex vector
space . Let be a locally quasi-nilpotent
elementary operator of length on . We show that, if
is locally linearly independent, then the local dimension of
V(\phi)=\spa\{b_ia_j: 1 \leq i,j \leq n\} is at most . If
\lDim V(\phi)=\frac{n(n-1)}{2} , then there exists a representation of
as with for . Moreover, we
give a complete characterization of locally quasi-nilpotent elementary
operators of length 3.Comment: 15
A not so simple local multiplier algebra
We construct an AF-algebra such that its local multiplier algebra
does not agree with ,
thus answering a question raised by G.K. Pedersen in 1978.Comment: 18 page
Spectral isometries on non-simple C*-algebras
We prove that unital surjective spectral isometries on certain non-simple
unital C*-algebras are Jordan isomorphisms. Along the way, we establish several
general facts in the setting of semisimple Banach algebras.Comment: 7 pages; paper available since July 201
A comparison between the methods of apportionment using power indices: the case of the U.S. presidential election
In this paper, we compare the five more famous methods of apportionment, the methods of Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the well-known Banzhaf power index. The populations are the ones of the different States of the U.S. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population: this ensures that every citizen in the country gets the same power. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results.Banzhaf index, methods of apportionment, distances, balance population-power.
Configurations study for the Banzhaf and the Shapley-Shubik indices of power
How can we count and list all the Banzhaf or Shapley-Shubik index of power configurations for a given number of players? There is no formula in the literature that may give the cardinal of such a set, and moreover, even if this formula had existed, there is no formula which gives the configuration vectors. Even if we do not present such a formula, we present a methodology which enables to determine the set of configurations and its cardinality.
On the Chacteristic Numbers of Voting Games
This paper deals with the non-emptiness of the stability set for any proper voting game.We present an upper bound on the number of alternatives which guarantees the non emptiness of this solution concept. We show that this bound is greater than or equal to the one given by Le Breton and Salles [6] for quota games.voting game, core, stability set
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