Banach Algebra of Bounded Complex Radon Measures on Homogeneous Space

2020 ◽  
Vol 44 (5) ◽  
pp. 1429-1437
Author(s):  
T. Derikvand ◽  
R. A. Kamyabi-Gol ◽  
M. Janfada
Keyword(s):  
Banach Algebra ◽  
Homogeneous Space ◽  
Radon Measures ◽  
Bounded Complex

Algebras of measures on C-distinguished topological semigroups

1978 ◽  
Vol 84 (2) ◽  
pp. 323-336 ◽  
Author(s):  
H. A. M. Dzinotyiweyi
Keyword(s):  
Total Variation ◽  
Topological Semigroup ◽  
Continuous Mapping ◽  
Continuous Functions ◽  
Compact Set ◽  
Locally Compact ◽  
Radon Measures ◽  
Topological Semigroups ◽  
Bounded Complex ◽  
Complex Valued

Let S be a (jointly continuous) topological semigroup, C(S) the set of all bounded complex-valued continuous functions on S and M (S) the set of all bounded complex-valued Radon measures on S. Let (S) (or (S)) be the set of all µ ∈ M (S) such that x → │µ│ (x-1C) (or x → │µ│(Cx-1), respectively) is a continuous mapping of S into ℝ, for every compact set C ⊆ S, and . (Here │µ│ denotes the measure arising from the total variation of µ and the sets x-1C and Cx-1 are as defined in Section 2.) When S is locally compact the set Ma(S) was studied by A. C. and J. W. Baker in (1) and (2), by Sleijpen in (14), (15) and (16) and by us in (3). In this paper we show that some of the results of (1), (2), (14) and (15) remain valid for certain non-locally compact S and raise some new problems for such S.

scholarly journals 1-Algebra of a Locally Compact Groupoid

ISRN Algebra ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Massoud Amini ◽  
Alireza Medghalchi ◽  
Ahmad Shirinkalam
Keyword(s):  
Invariant Measure ◽  
Banach Algebra ◽  
Haar System ◽  
Locally Compact ◽  
Radon Measures ◽  
Integrable Functions

For a locally compact groupoid with a fixed Haar system and quasi-invariant measure , we introduce the notion of -measurability and construct the space 1(, , ) of absolutely integrable functions on and show that it is a Banach -algebra and a two-sided ideal in the algebra () of complex Radon measures on . We find correspondences between representations of on Hilbert bundles and certain class of nondegenerate representations of 1(, , ).

Some results on the union of Helson sets

1971 ◽  
Vol 70 (2) ◽  
pp. 235-241
Author(s):  
E. Galanis
Keyword(s):  
Abelian Group ◽  
Compact Subset ◽  
Compact Abelian Group ◽  
Dual Group ◽  
Radon Measures ◽  
Bounded Complex ◽  
Complex Valued

Let G be a compact abelian group and let Ĝ be its dual group. We shall denote by M(G) the set of all bounded complex valued Radon measures on G and by M(E) the elements of M(G) with support in a compact subset E of G.

The Wiener–Pitt phenomenon on semi-groups

1963 ◽  
Vol 59 (1) ◽  
pp. 11-24 ◽  
Author(s):  
T. A. Davis
Keyword(s):  
Abelian Group ◽  
Banach Algebra ◽  
Haar Measure ◽  
Group Algebra ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Bounded Complex ◽  
Additive Measures ◽  
Complex Valued

Let G be a locally compact Abelian group, written adoptively, with Haar measure m, L1(G) the group algebra of G, and M(G) the Banach algebra of all bounded, complex-valued, regular, countably additive measures on G. For a general account of L1(G) and M(G) see Rudin (7).

scholarly journals Banach Algebra of Bounded Complex-Valued Functionals

2011 ◽  
Vol 19 (2) ◽  
pp. 121-126 ◽  
Author(s):  
Katuhiko Kanazashi ◽  
Hiroyuki Okazaki ◽  
Yasunari Shidama
Keyword(s):  
Banach Algebra ◽  
Basic Properties ◽  
Bounded Complex ◽  
Complex Valued

Banach Algebra of Bounded Complex-Valued Functionals In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded complex-valued functionals.

Lossless bounded complex digital two-pair

1988 ◽  
Vol 24 (24) ◽  
pp. 1513
Author(s):  
J.I. Acha ◽  
F. Torres
Keyword(s):  
Bounded Complex

scholarly journals Character on a homogeneous space

2021 ◽  
Vol 131 (1) ◽  
Author(s):  
A J Parameswaran ◽  
K Amith Shastri
Keyword(s):  
Homogeneous Space

ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS

2021 ◽  
pp. 1-12
Author(s):  
PRAKASH A. DABHI ◽  
DARSHANA B. LIKHADA
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Discrete Groups ◽  
Discrete Semigroups ◽  
Beurling Algebras

Abstract Let $(G_1,\omega _1)$ and $(G_2,\omega _2)$ be weighted discrete groups and $0\lt p\leq 1$ . We characterise biseparating bicontinuous algebra isomorphisms on the p-Banach algebra $\ell ^p(G_1,\omega _1)$ . We also characterise bipositive and isometric algebra isomorphisms between the p-Banach algebras $\ell ^p(G_1,\omega _1)$ and $\ell ^p(G_2,\omega _2)$ and isometric algebra isomorphisms between $\ell ^p(S_1,\omega _1)$ and $\ell ^p(S_2,\omega _2)$ , where $(S_1,\omega _1)$ and $(S_2,\omega _2)$ are weighted discrete semigroups.

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