partial actions and kms states on relative graph c algebras abstract the relative graph c algebras introduced by muhly and tomforde are generalizations of both graph algebras and their toeplitz extensions for an arbitrary graph e and a subset r of the set of regular vertices of e we show that the relative graph c algebra c e r is isomorphic to a partial crossed product for an action of the free group generated by the edge set on the relative boundary path space given a time evolution on c e r induced by a function on the edge set we characterize the kms states and ground states using an abstract result of exel and laca guided by their work on kms states for toeplitz cuntz krieger type algebras associated to infinite matrices we obtain complete descriptions of the convex sets of kms states of finite type and of kms states of infinite type whose associated measures are supported on recurrent infinite paths this allows us to give a complete concrete description of the convex set of all kms states for a big class of graphs which includes all graphs with finitely many vertices

kms weights on graph c algebras abstract the paper contains a study of the gauge invariant kms weights for a generalized gauge action on a graph c algebra when the graph is irreducible and has the property that there are at most countably many roads to infinity in the graph a complete description is given of the structure of kms weights for the gauge action the structure is very rich and is identical with the structure of kms states for the restriction of the action to any corner defined by a projection in the fixed point algebra

reduced solutions of douglas equations and angles between subspaces in this paper we study some particular solutions of douglas type equations by means of generalized inverses and angles we apply this result to characterize positive solutions and some special projections which are symmetrizable for a semidefinited positive bounded linear operator

on the c algebra of a locally injective surjection and its kms states it is shown that a locally injective surjection on a compact metric space is a factor of a local homeomorphism in such a way that the associated c algebras are isomorphic this is subsequently used to obtain upper and lower bounds for the possible values of kms states for generalized gauge actions on the c algebra

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

the moore penrose inverses of products and differences of projections in a c algebra abstract for two given projections p and q in a c algebra we investigate how to express moore penrose inverses of products pq and differences p q and pq qp moreover it is shown that pq qp is moore penrose invertible if and only if pq and p q are moore penrose invertible in addition some related topics are considered

groupoids associated with endomorphisms to a compact hausdorff space which covers itself we associate an r discrete locally compact hausdorff groupoid its c algebra carries an action of the circle allowing it to be regarded as a crossed product by an endomorphism and as a generalization of the cuntz algebra op we consider examples related to coverings of the circle and of a heisenberg 3 manifold given a compact hausdorff space x and a continuous surjective map a x x we want to associate to the pair x a a c algebra c x a which in the case a is a homeomorphism coincides with the well known crossed product c x x z in this paper we consider the case of a covering a x x and c x a will be defined via a groupoid that generalizes the construction of the cuntz groupoid op considered by renault in re in that case x is a unilateral sequence space and a is the unilateral shift we start with some definitions and notation that make sense in greater generality definition given a set x and a map a x x let i x n y e xx zx x i 3k 1 0 n i k akx aly with the set of composable pairs i 2 x n y w m z e jx j w y the multiplication and inversion are given by x n y y m z x m n z and x n y 1 y n x the range and source maps are r x n y x 0 x s x n y y 0 y with these operations if becomes a groupoid with the unit space identified with x the equivalence relation associated to if will be denoted by r where r x y e x x x i 3k 1 0 akx ly and the isotropy group bundle is i x n x exxzxx ik 1 0 n l k akx alx received by the editors march 25 1993 and in revised form january 21 1994 originally communicated to the proceedings of the ams by palle e t jorgensen 1991 mathematics subject classification primary 46l05 46l55 46l80 research supported in part by the national science foundation 1995 american mathematical society 0002 9947 95 1 00 25 per page

kms weights on groupoid and graph c algebras abstract the paper contains a description of the kms weights for the one parameter action on the reduced c algebra of a second countable locally compact hausdorff etale groupoid arising from a continuous real valued homomorphism satisfying two conditions the result is subsequently applied to identify the kms weights for the gauge action on a simple graph algebra the von neumann algebra generated by the gns representation of an extremal kms weight is a factor and tools are developed to determine its type the paper concludes with three examples to illustrate the results

groetsch s representation of moore penrose inverses and ill posed problems in hilbert c modules abstract the explicit representation lim 0 1 t t 1 t for the moore penrose inverse of an operator t between hilbert spaces has been given by c w groetsch 1975 6 we obtain his formula for the moore penrose inverse of an unbounded operator between hilbert c modules ill posed problems with unbounded operator between hilbert c modules are also discussed

partial dynamical systems and the kms condition given a countably infinite 0 1 matrix a without identically zero rows let a be the cuntz krieger algebra recently introduced by the authors and a be the toeplitz extension of a once the latter is seen as a cuntz pimsner algebra as recently shown by szymanski we study the kms equilibrium states of c dynamical systems based on a and a with dynamics satisfying for the canonical generating partial isometries s x and arbitrary real numbers n x 1 the kms states on both a and a are completely characterized for certain values of the inverse temperature according to the position of relative to three critical values defined to be the abscissa of convergence of certain dirichlet series associated to a and the n x our results for a are derived from those for a by virtue of the former being a covariant quotient of the latter when the matrix a is finite these results give theorems of olesen and pedersen for n and of enomoto fujii and watatani for a as particular cases

maps preserving semi fredholm operators on hilbert c modules abstract let m be a hilbert c module over the c algebra a and l a m the c algebra of all adjointable operators on m let l a m l a m be a unital linear map preserving semi a fredholm operators in both directions and assume that is surjective up to compact operators we will show that preserves compact operators and in certain cases the induced map l a m k a m l a m k a m is an automorphism or an anti automorphism

the product of operators with closed range in hilbert c modules abstract suppose t and s are bounded adjointable operators with close range between hilbert c modules then ts has closed range if and only if ker t ran s is an orthogonal summand if and only if ker s ran t is an orthogonal summand moreover if the dixmier or minimal angle between ran s and ker t ker t ran s is positive and ker s ran t is an orthogonal summand then ts has closed range

characterizations and representations of the group inverse involving idempotents this paper is to present some results on the group invertibility of products and differences of idempotents in addition some formulae for the group inverse of sums differences and products of idempotents are established by using some given idempotents

concentration of source terms in generalized glimm scheme for global entropy solutions of nonlinear hyperbolic balance laws abstract in this paper we investigate the cauchy problem for a nonlinear hyperbolic system of balance laws with sources a x g and a t h to get the approximate solutions of our problem we consider a version of generalized riemann problem that concentrates the variation of a on a thin t shaped region of each grid a new version of glimm scheme is introduced to construct the approximate solutions and its stability is proved by considering two types of conditions on a finally we verify the consistency of the scheme and the entropy inequality to establish the global existence of entropy solutions

positive semi definite matrices of adjointable operators on hilbert c modules abstract let a be a c algebra h k be two hilbert a modules and b be an adjointable operator from h to k in this paper we prove that the moore penrose inverse of b exists if and only if b has closed range in addition some known results about the moore penrose inverses acting on hilbert spaces as well as in c algebras are extended in the context of hilbert c modules as an application a characterization of positive semi definite matrices of adjointable operators with respect to an orthogonal pair of a hilbert c module is given

on the existence of conformal measures a general notion of conformal measure is introduced and some basic properties are studied sufficient conditions for the existence of these measures are obtained using a general construction principle the geometric properties of conformal measures relate equilibrium states and hausdorff measures this is shown for invariant subsets of s under expanding maps

descriptions of partial isometries on hilbert c modules abstract partial isometries and moore penrose inverses of bounded adjointable operators on hilbert c modules are investigated it is shown that a contraction between hilbert c modules is a partial isometry if and only if it possesses a contractive moore penrose inverse a bounded adjointable operator t is a partial isometry if and only if its bounded transform is 2 1 2 t

finite digraphs and kms states abstract the paper contains a description of the kms states of a generalized gauge action on the c algebra of a finite graph

kms states on the c algebras of finite graphs abstract we consider a finite directed graph e and the gauge action on its toeplitz cuntz krieger algebra viewed as an action of r for inverse temperatures larger than a critical value c we give an explicit construction of all the kms states if the graph is strongly connected then there is a unique kms c state and this state factors through the quotient map onto c e our approach is direct and relatively elementary

common hermitian and positive solutions to the adjointable operator equations ax c xb d let a be a c algebra for any hilbert a modules h and k let l h k be the set of adjointable operators from h to k let h k l be hilbert a modules a c l h k and b d l l h in this paper we propose necessary and sufficient conditions for the existence of common hermitian and positive solutions x l h to the equations ax c xb d and obtain the formulae for the general forms of these solutions some results known for finite matrices and hilbert space operators are extended to the adjointable operators acting on hilbert c modules