On the Homeomorphic Affine Embedding of a Locally Compact Cone into a Banach Dual Space Endowed with the Vague Topology

1964 ◽  
Vol s3-14 (3) ◽  
pp. 399-414 ◽  
Author(s):  
D. A. Edwards
Keyword(s):  
Dual Space ◽  
Locally Compact ◽  
Affine Embedding

scholarly journals ON HOMOLOGICAL PROPERTIES FOR SOME MODULES OF UNIFORMLY CONTINUOUS FUNCTIONS OVER CONVOLUTION ALGEBRAS

2011 ◽  
Vol 84 (2) ◽  
pp. 177-185
Author(s):  
RASOUL NASR-ISFAHANI ◽  
SIMA SOLTANI RENANI
Keyword(s):  
Compact Group ◽  
Group Algebra ◽  
Dual Space ◽  
Continuous Functions ◽  
Locally Compact Group ◽  
Measure Algebra ◽  
Locally Compact ◽  
Convolution Algebras ◽  
Uniformly Continuous

AbstractFor a locally compact group G, let LUC(G) denote the space of all left uniformly continuous functions on G. Here, we investigate projectivity, injectivity and flatness of LUC(G) and its dual space LUC(G)* as Banach left modules over the group algebra as well as the measure algebra of G.

scholarly journals Order Structure of the Figà-Talamanca-Herz Algebra

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Marzieh Shams Yousefi ◽  
Massoud Amini ◽  
Fereshteh Sady
Keyword(s):  
Dual Space ◽  
Space Structure ◽  
Locally Compact Group ◽  
Order Structure ◽  
Locally Compact ◽  
Completely Positive ◽  
Algebra Isomorphism ◽  
Positive Linear Map ◽  
Operator Space Structure ◽  
And Algebra

We study the interplay between the order structure and the -operator space structure of Figà-Talamanca-Herz algebra of a locally compact group . We show that for amenable groups, an order and algebra isomorphism of Figà-Talamanca-Herz-algebras yields an isomorphism or anti-isomorphism of the underlying groups. We also give a bound for the norm of a -completely positive linear map from Figà-Talamanca-Herz algebra to its dual space.

Weak Containment and Induced Representations of Groups

1962 ◽  
Vol 14 ◽  
pp. 237-268 ◽  
Author(s):  
J. M. G. Fell
Keyword(s):  
Dual Space ◽  
Locally Compact Group ◽  
Equivalence Classes ◽  
Unitary Representations ◽  
Unitary Equivalence ◽  
Locally Compact ◽  
Induced Representations ◽  
Weak Containment ◽  
Irreducible Unitary Representations ◽  
Special Case

Let G be a locally compact group and G† its dual space, that is, the set of all unitary equivalence classes of irreducible unitary representations of G. An important tool for investigating the group algebra of G is the so-called hull-kernel topology of G†, which is discussed in (3) as a special case of the relation of weak containment. The question arises: Given a group G, how do we determine G† and its topology? For many groups G, Mackey's theory of induced representations permits us to catalogue all the elements of G†. One suspects that by suitably supplementing this theory it should be possible to obtain the topology of G† at the same time. It is the purpose of this paper to explore this possibility. Unfortunately, we are not able to complete the programme at present.

The Duality of Distributive Continuous Lattices

1980 ◽  
Vol 32 (2) ◽  
pp. 385-394 ◽  
Author(s):  
B. Banaschewski
Keyword(s):  
Dual Space ◽  
Boolean Algebras ◽  
Distributive Lattices ◽  
Continuous Lattice ◽  
Prime Spectrum ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Continuous Lattices ◽  
Prime Elements

Various aspects of the prime spectrum of a distributive continuous lattice have been discussed extensively in Hofmann-Lawson [7]. This note presents a perhaps optimally direct and self-contained proof of one of the central results in [7] (Theorem 9.6), the duality between distributive continuous lattices and locally compact sober spaces, and then shows how the familiar dualities of complete atomic Boolean algebras and bounded distributive lattices derive from it, as well as a new duality for all continuous lattices. As a biproduct, we also obtain a characterization of the topologies of compact Hausdorff spaces.Our approach, somewhat differently from [7], takes the open prime filters rather than the prime elements as the points of the dual space. This appears to have conceptual advantages since filters enter the discussion naturally, besides being a well-established tool in many similar situations.

scholarly journals The predual of the space of convolutors on a locally compact group

1998 ◽  
Vol 57 (3) ◽  
pp. 409-414 ◽  
Author(s):  
Michael Cowling
Keyword(s):  
Compact Group ◽  
Maximal Ideal ◽  
Lebesgue Space ◽  
Dual Space ◽  
Locally Compact Group ◽  
Ideal Space ◽  
Convolution Operators ◽  
Locally Compact ◽  
Algebra Of Functions ◽  
Definition Of

Let Cvp(G) be the space of convolution operators on the Lebesgue space LP(G), for an arbitrary locally compact group G. We describe Cvp(G) as a dual space, whose predual, is a Banach algebra of functions on G, under pointwise operations, with maximal ideal space G. This involves a variation of Herz's definition of AP(G); the benefit of this new definition is that all of Cvp(G) is obtained as the dual in the nonamenable setting. We also discuss further developments of this idea.

scholarly journals Covariant functions of characters of compact subgroups

2021 ◽  
Vol 12 (3) ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Compact Group ◽  
Harmonic Analysis ◽  
Banach Spaces ◽  
Systematic Study ◽  
Dual Space ◽  
Quotient Space ◽  
Compact Subgroup ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Conjugate Exponent

AbstractThis paper presents a systematic study for abstract harmonic analysis on classical Banach spaces of covariant functions of characters of compact subgroups. Let G be a locally compact group and H be a compact subgroup of G. Suppose that $$\xi :H\rightarrow \mathbb {T}$$ ξ : H → T is a character, $$1\le p<\infty$$ 1 ≤ p < ∞ and $$L_\xi ^p(G,H)$$ L ξ p ( G , H ) is the set of all covariant functions of $$\xi$$ ξ in $$L^p(G)$$ L p ( G ) . It is shown that $$L^p_\xi (G,H)$$ L ξ p ( G , H ) is isometrically isomorphic to a quotient space of $$L^p(G)$$ L p ( G ) . It is also proven that $$L^q_\xi (G,H)$$ L ξ q ( G , H ) is isometrically isomorphic to the dual space $$L^p_\xi (G,H)^*$$ L ξ p ( G , H ) ∗ , where q is the conjugate exponent of p. The paper is concluded by some results for the case that G is compact.

Sign in / Sign up

Export Citation Format

Share Document