Iranian Journal of Mathematical Sciences and Informatics
Year:2011 | Volume:6 | Issue:2|Papers Count:8

A basic relation between numerical range and Davis-Wielandt shell of an operatorA acting on a Hilbert space with orthonormal basis  e= [ei|I ϵ I} and its conjugate A- which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of A and A-. A necessary and sufficient condition for A to be self-conjugate (A=A-) is given using a subgroup of H.

In this paper we introduce a special form of symmetric matrices that is called central symmetric X-form matrix and study some of their properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

We investigate shift invariant subspaces of L2 (G), where G is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift invariant subspaces of L2 (G) in terms of range functions. Finally, we investigate shift preserving operators on locally compact abelian groups. We show that there is a one-to-one correspondence between shift preserving operators and range operators on L2 (G) where Gis a locally compact abelian group.

This paper is devoted to deformation theory of “anabelian” representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for functors on Artin local rings. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic applications.

For vectors X, Y ϵ Rn, we say X is left matrix majorized by Y and write X<eY if for some row stochastic matrix R, X=RY. Also, we write X~eY, when X<eY<eX. A linear operator T: Rp®Rn is said to be a linear preserver of a given relation<if X<Y on Rp implies that TX<TY on Rn. In this note we study linear preservers of ~e from Rp to Rn. In particular, we characterize all linear preservers of ~e from R2 to Rn, and also, all linear preservers of ~e from Rp to Rp.

In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, direct products and direct limits of groups with topological approach.

The distance d (u, v) between two vertices u and v of a graph Gis equal to the length of a shortest path that connects u and v. Define WW (G, x) =1/2 S [a, b]ÍV (G) x d (a, b)+d2 (a, b), where d (G) is the greatest distance between any two vertices. In this paper the hyper-Wiener polynomials of the Cartesian product, composition, join and disjunction of graphs are computed.

Let R be a commutative ring with Z (R) its set of zero-divisors. In this paper, we study the total graph of R, denoted by T (G (R)). It is the (undirected) graph with all elements of R as vertices, and for distinct x, yÎR, the vertices x and y are adjacent if and only if x+y Î Z (R). We study the chromatic number and edge connectivity of this graph.