Weak-star continuous homomorphisms and a decomposition of orthogonal measures

B. J. Cole; Theodore W. Gamelin

Annales de l'institut Fourier (1985)

  • Volume: 35, Issue: 1, page 149-189
  • ISSN: 0373-0956

Abstract

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We consider the set S ( μ ) of complex-valued homomorphisms of a uniform algebra A which are weak-star continuous with respect to a fixed measure μ . The μ -parts of S ( μ ) are defined, and a decomposition theorem for measures in A ⊥ ∩ L 1 ( μ ) is obtained, in which constituent summands are mutually absolutely continuous with respect to representing measures. The set S ( μ ) is studied for T -invariant algebras on compact subsets of the complex plane and also for the infinite polydisc algebra.

How to cite

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Cole, B. J., and Gamelin, Theodore W.. "Weak-star continuous homomorphisms and a decomposition of orthogonal measures." Annales de l'institut Fourier 35.1 (1985): 149-189. <http://eudml.org/doc/74663>.

@article{Cole1985,
abstract = {We consider the set $S(\mu )$ of complex-valued homomorphisms of a uniform algebra $A$ which are weak-star continuous with respect to a fixed measure $\mu $. The $\mu $-parts of $S(\mu )$ are defined, and a decomposition theorem for measures in $A^\{\perp \}\cap L^ 1(\mu )$ is obtained, in which constituent summands are mutually absolutely continuous with respect to representing measures. The set $S(\mu )$ is studied for $T$-invariant algebras on compact subsets of the complex plane and also for the infinite polydisc algebra.},
author = {Cole, B. J., Gamelin, Theodore W.},
journal = {Annales de l'institut Fourier},
keywords = {uniform algebra; T-invariant algebras; infinite polydisc algebra},
language = {eng},
number = {1},
pages = {149-189},
publisher = {Association des Annales de l'Institut Fourier},
title = {Weak-star continuous homomorphisms and a decomposition of orthogonal measures},
url = {http://eudml.org/doc/74663},
volume = {35},
year = {1985},
}

TY - JOUR
AU - Cole, B. J.
AU - Gamelin, Theodore W.
TI - Weak-star continuous homomorphisms and a decomposition of orthogonal measures
JO - Annales de l'institut Fourier
PY - 1985
PB - Association des Annales de l'Institut Fourier
VL - 35
IS - 1
SP - 149
EP - 189
AB - We consider the set $S(\mu )$ of complex-valued homomorphisms of a uniform algebra $A$ which are weak-star continuous with respect to a fixed measure $\mu $. The $\mu $-parts of $S(\mu )$ are defined, and a decomposition theorem for measures in $A^{\perp }\cap L^ 1(\mu )$ is obtained, in which constituent summands are mutually absolutely continuous with respect to representing measures. The set $S(\mu )$ is studied for $T$-invariant algebras on compact subsets of the complex plane and also for the infinite polydisc algebra.
LA - eng
KW - uniform algebra; T-invariant algebras; infinite polydisc algebra
UR - http://eudml.org/doc/74663
ER -

References

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  13. [13]I. GLICKSBERG, Equivalence of certain representing measures, Proc. A.M.S., 82 (1981), 374-376. Zbl0483.46029MR83j:46066
  14. [14]K. HOFFMAN and H. ROSSI, Extension of positive weak*-continuous functionals, Duke Math. J., 34 (1967), 453-466. Zbl0155.45701MR37 #763
  15. [15]H. KONIG and G.L. SEEVER, The abstract F. and M Riesz theorem, Duke Math. J., 36 (1969), 791-797. Zbl0201.45704MR44 #4526
  16. [16]T. LYONS, Finely holomorphic functions, J. Funct. Anal., 37 (1980), 1-18. Zbl0459.46038MR82d:31011a
  17. [17]D.E. SARASON, Weak-star density of polynomials, J. Reine Angew Math., 252 (1972), 1-15. Zbl0242.46023MR45 #4156

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