261 research outputs found
Presentations for monoids of finite partial isometries
In this paper we give presentations for the monoid of all
partial isometries on and for its submonoid
of all order-preserving partial isometries.Comment: 11 pages, submitte
Subproduct systems and Cartesian systems; new results on factorial languages and their relations with other areas
We point out that a sequence of natural numbers is the dimension sequence of
a subproduct system if and only if it is the cardinality sequence of a word
system (or factorial language). Determining such sequences is, therefore,
reduced to a purely combinatorial problem in the combinatorics of words. A
corresponding (and equivalent) result for graded algebras has been known in
abstract algebra, but this connection with pure combinatorics has not yet been
noticed by the product systems community. We also introduce Cartesian systems,
which can be seen either as a set theoretic version of subproduct systems or an
abstract version of word systems. Applying this, we provide several new results
on the cardinality sequences of word systems and the dimension sequences of
subproduct systems.Comment: New title; added references; to appear in Journal of Stochastic
Analysi
Amalgams of Inverse Semigroups and C*-algebras
An amalgam of inverse semigroups [S,T,U] is full if U contains all of the
idempotents of S and T. We show that for a full amalgam [S,T,U], the C*-algebra
of the inverse semigroup amaglam of S and T over U is the C*-algebraic amalgam
of C*(S) and C*(T) over C*(U). Using this result, we describe certain
amalgamated free products of C*-algebras, including finite-dimensional
C*-algebras, the Toeplitz algebra, and the Toeplitz C*-algebras of graphs
Diffusion determines the recurrent graph
We consider diffusion on discrete measure spaces as encoded by Markovian
semigroups arising from weighted graphs. We study whether the graph is uniquely
determined if the diffusion is given up to order isomorphism. If the graph is
recurrent then the complete graph structure and the measure space are
determined (up to an overall scaling). As shown by counterexamples this result
is optimal. Without the recurrence assumption, the graph still turns out to be
determined in the case of normalized diffusion on graphs with standard weights
and in the case of arbitrary graphs over spaces in which each point has the
same mass. These investigations provide discrete counterparts to studies of
diffusion on Euclidean domains and manifolds initiated by Arendt and continued
by Arendt/Biegert/ter Elst and Arendt/ter Elst. A crucial step in our
considerations shows that order isomorphisms are actually unitary maps (up to a
scaling) in our context.Comment: 30 page
- …