The dual spaces of *-algebras

@article{Fell1960TheDS,
  title={The dual spaces of *-algebras},
  author={J. M. G. Fell},
  journal={Transactions of the American Mathematical Society},
  year={1960},
  volume={94},
  pages={365-403}
}
  • J. Fell
  • Published 1 March 1960
  • Mathematics
  • Transactions of the American Mathematical Society
Introduction. The idea of the structure space (or dual space) A of an associative algebra A was introduced by Jacobson in [8]. The space A consists of all kernels of irreducible representations of A, with the hull-kernel topology: An ideal I in A is in the closure of a subset B of A if I contains the intersection of the ideals in B. For unrestricted infinite-dimensional A, the dual space need not be Hausdorff or even T1; and in many situations it is not very useful. However, Gelfand and others… 
THE DUAL SPACES OF BANACH ALGEBRAS
Introduction. A great deal of work has been done in the last fifteen years on the theory and classification of irreducible unitary representations of locally compact groups. It is also generally
TOPOLOGICAL REPRESENTATION OF C*-ALGEBRAS
Let A be a C*-algebra, ίl the structure space of A, i.e. the space of all primitive ideals in A with hull-kernel topology. At every point P of ί l we associate a primitive C^-algebra A/P (which we
A description of the topology on the dual spaces of certain locally compact groups
Introduction. Suppose G is a locally compact group. By the dual space G of G we mean the set of all equivalence classes of irreducible unitary representations of G equipped with the "hull-kernel"
WEAK CONTAINMENT AND INDUCED REPRESENTATIONS OF GROUPS. II(
Introduction. In [6] we have outlined a program for determining the structure of an arbitrary C*-algebra A in terms of its primitive images. The first step in this program is always to determine the
The structure of standard C∗-algebras and their representations
!• Introduction* The Wedderburn structure theorem asserts that every finite dimensional complex semi-simple algebra is a di rect sum of simple algebras, each of which is an n x n matrix algebra. The
Finite-dimensional representations of JB algebras
Let A be the set of isomorphism classes of finite dimensional JB factors, ordered by inclusion. For any a E A and JB algebra 6f denote by a(i the set of equivalence classes of factor representations
A decomposition theory for unitary representations of locally compact groups
Introduction. In the classical theory of finite dimensional representations of compact groups, every representation may be expressed uniquely as a direct sum of irreducible representations. This
On derivations and elementary operators on C*-algebras
  • Ilja Gogić
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 2013
Abstract Let A be a unital C*-algebra with the canonical (H) C*-bundle $\mathfrak{A}$ over the maximal ideal space of the centre of A, and let E(A) be the set of all elementary operators on A. We
Unitary Representations of Groups, Duals, and Characters
This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions
...
...

References

SHOWING 1-10 OF 14 REFERENCES
Borel structure in groups and their duals
Introduction. In the past decade or so much work has been done toward extending the classical theory of finite dimensional representations of compact groups to a theory of (not necessarily finite
Groups with Representations of Bounded Degree
Let G be a compact group. According to the celebrated theorem of Peter-Weyl there exists a complete set of finite-dimensional irreducible unitary representations of G, the completeness meaning that
A theory of spherical functions. I
The fact that there exists a close connection between the classical theory of spherical harmonics and that of group representations was first established by E. Cartan and H. Weyl in well known
A Topology for the Set of Primitive Ideals in an Arbitrary Ring.
  • N. Jacobson
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1945
TLDR
The Wedderburn-Artin structure theorem on simple rings satisfying the descending chain condition the authors have the theorem that if 21 is a primitive ring 7 0, W1 is isomorphic to a dense ring of linear transformations in a suitable vector space over a division ring.
Normed Linear Spaces
Each of the function spaces mentioned in the introduction of the preceding chapter has (with one exception, A(D)) a norm ∥ ∥ [Definition I, 3, 1] which defines the topology of major interest in the
An Introduction to Abstract Harmonic Analysis
TLDR
An introduction to abstract harmonic analysis is one of the literary work in this world in suitable to be reading material and it will show you the amazing benefits of reading a book.
Les fonctions de type positif et la théorie des groupes
La théorie des groupes topologiques, bien que de création récente, constitue aujourd'hui une branche importante des mathématiques; elle englobe des théories comme: la mesure de Haar, la théorie du
Sur la Theorie des Representations Unitaires
Le but de ce travail est de pr6senter quelques r6sultats nouveaux-ainsi que d'autres-relatifs A la th6orie des representations unitaires des algebres involutives. Le Chapitre I concerne la th6orie
...
...