scholarly journals Complete continuity properties of Banach spaces associated with subsets of a discrete abelian group

2001 ◽  
Vol 43 (02) ◽  
Author(s):  
Mangatiana A. Robdera ◽  
Paulette Saab
Keyword(s):  
Abelian Group ◽  
Banach Spaces ◽  
Complete Continuity ◽  
Continuity Properties ◽  
Discrete Abelian Group

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

scholarly journals The Spectral Radius Formula for Fourier–Stieltjes Algebras

2019 ◽  
Vol 63 (2) ◽  
pp. 269-275
Author(s):  
Przemysław Ohrysko ◽  
Maria Roginskaya
Keyword(s):  
Abelian Group ◽  
Spectral Radius ◽  
Haar Measure ◽  
Short Note ◽  
Measure Algebra ◽  
Stieltjes Transform ◽  
Locally Compact ◽  
Convolution Powers ◽  
Discrete Abelian Group ◽  
Spectral Radius Formula

AbstractIn this short note we first extend the validity of the spectral radius formula, obtained by M. Anoussis and G. Gatzouras, for Fourier–Stieltjes algebras. The second part is devoted to showing that, for the measure algebra on any locally compact non-discrete Abelian group, there are no non-trivial constraints among three quantities: the norm, the spectral radius, and the supremum of the Fourier–Stieltjes transform, even if we restrict our attention to measures with all convolution powers singular with respect to the Haar measure.

23.—Weak Continuity Properties of Mappings and Semigroups

1975 ◽  
Vol 72 (4) ◽  
pp. 275-280 ◽  
Author(s):  
J. M. Ball
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Weak Continuity ◽  
Continuity Properties ◽  
The Relationship

SynopsisThe relationship between weak and sequential weak continuity for mappings between Banach spaces and semigroups on Banach space is studied.

Multipliers for vector valued functions

1984 ◽  
Vol 99 (1-2) ◽  
pp. 137-143
Author(s):  
José Luis Torrea
Keyword(s):  
Abelian Group ◽  
Banach Spaces ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
Translation Invariant ◽  
Bounded Linear ◽  
Vector Valued Functions ◽  
Vector Valued

SynopsisLet G be a locally compact abelian group and let Γ be the dual of G. Let A, B be Banach spaces and Lp(G,A) the Bochner-Lebesgue spaces. We prove that the space of bounded linear translation invariant operators from L1(G, A) to LX(G, B) can be identified with the space of bounded convolution invariant (in some sense) operators and also with the space of a(A, B)-valued “weak regular” measures with the relation Tf = f *μ. (A. The existence of a function m∈ L∞ (Γ,α(A,B)), such that is also proved.

Continuous singular measures equivalent to their convolution squares

1976 ◽  
Vol 80 (2) ◽  
pp. 249-268 ◽  
Author(s):  
Gavin Brown ◽  
Edwin Hewitt
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Measure Algebra ◽  
Locally Compact ◽  
Character Group ◽  
Singular Measures ◽  
Continuous Measures ◽  
Discrete Abelian Group

Throughout this paper, G will denote a locally compact, non-discrete, Abelian group (subjected to various conditions) and X wi11 denote the character group of G. All terminology and notation are as in (7). The measure algebra M(G), as is known, is a very complicated entity. We address ourselves here to some novel peculiarities of the subspace Ms(G) of continuous measures in M(G) that are singular with respect to Haar measure λ.

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