Search results for " Mathematics"

Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifolds

2003

For appropriate triples (M, g, M), where M is an (in general non-compact) manifold, g is a metric on T*M, and M is a weight function on T* M, we developed in [5] a pseudo-differential calculus on.A.4 which is based on the S(M, g)-calculus of L. Hormander [30] in local models. Here we prove that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [21] in \( \mathcal{L}\left( {{L^2}\left( M \right)} \right)\). For the basic calculus we generalized the concept of E. Schrohe [40] of so-called SG-compatible manifolds. In the proof of the existence of “order reducing operators” we apply a method from [4], and the proof of spectral invariance and sub…

Convergence-theoretic mechanisms behind product theorems

2000

Abstract Commutation of the topologizer with products, quotientness of product maps, preservation of some properties by products, topologicity of continuous convergence, continuity of complete lattices are facets of the same quest. A new method of multifilters is used to establish (in terms of core-contour-compactness) sufficient and necessary conditions for these properties in the framework of general convergences. The relativized Antoine reflector plays here an important role. Several classical results (of Whitehead, Michael, Boehme, Cohen, Day and Kelly, Hofmann and Lawson, Schwarz and Weck, Kent and Richardson, and others) are extended or refined.

OnK 0-functions and regular extension operators

1992

Faithful representations of left C*-modules

2010

The existence of a faithful modular representation of a left module $$ \mathfrak{X} $$ over a C*-algebra $$ \mathfrak{A}_\# $$ possessing sufficiently many traces is proved.

Elliptic convolution operators on non-quasianalytic classes

2001

For those nonquasianalytic classes in which an extension of the classical Borel's theorem holds we show that every elliptic convolution operator is the composition of a translation and an invertible ultradifferential operator. This answers a question asked by Chou in: La transformation de Fourier complexe et l'equation de convolution, LNM 325, Berlin-Heidelberg-New York (1973).

Some seminorms on quasi*-algebras

2003

Dieren t types of seminorms on a quasi -algebra (A; A0) are constructed from a suitable family F of sesquilinear forms on A. Two particular classes, extended C -seminorms and CQ -seminorms, are studied in some detail. A necessary and sucien t condition for the admissibility of a sesquilinear form in terms of extended C -seminorms on (A; A0) is given.

Nondivisibility among character degrees II: Nonsolvable groups

2007

We say that a finite group G is an NDAD-group (no divisibility among degrees) if for any 1 < a < b in the set of degrees of the complex irreducible characters of G, a does not divide b. In this article, we determine the nonsolvable NDAD-groups. Together with the work of Lewis, Moreto and Wolf (J. Group Theory 8 (2005)), this settles a problem raised by Berkovich and Zhmud’, which asks for a classification of the NDAD-groups.

A general characterization of the Janko simple groupJ 2

1974

Confined subgroups in periodic simple finitary linear groups

2002

A subgroupX of the locally finite groupG is said to beconfined, if there exists a finite subgroupF≤G such thatX g∩F≠1 for allg∈G. Since there seems to be a certain correspondence between proper confined subgroups inG and non-trivial ideals in the complex group algebra ℂG, we determine the confined subgroups of periodic simple finitary linear groups in this paper.

Closure operations for Schunck classes and formations of finite solvable groups

1979

The purpose of the present note is to investigate the closure operations common to both the operations of forming classes and formations. Furthermore, new descriptions of formations and saturated formations in terms of closure operations are given.