Some remarks on Q -algebras

Nicolas Th. Varopoulos

Annales de l'institut Fourier (1972)

  • Volume: 22, Issue: 4, page 1-11
  • ISSN: 0373-0956

Abstract

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We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that p , ( 1 p ) are Q algebras and that A n = L 1 ( Z ; 1 + | n | α ) is a Q -algebra if and only if α > 1 / 2 .

How to cite

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Varopoulos, Nicolas Th.. "Some remarks on $Q$-algebras." Annales de l'institut Fourier 22.4 (1972): 1-11. <http://eudml.org/doc/74099>.

@article{Varopoulos1972,
abstract = {We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that $\ell ^p$, $(1\le p \le \infty )$ are $Q$ algebras and that $A_n = \{\frak Z\}L^1(\{\bf Z\};1+|n|^\alpha )$ is a $Q$-algebra if and only if $\alpha &gt; 1/2$.},
author = {Varopoulos, Nicolas Th.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {1-11},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some remarks on $Q$-algebras},
url = {http://eudml.org/doc/74099},
volume = {22},
year = {1972},
}

TY - JOUR
AU - Varopoulos, Nicolas Th.
TI - Some remarks on $Q$-algebras
JO - Annales de l'institut Fourier
PY - 1972
PB - Association des Annales de l'Institut Fourier
VL - 22
IS - 4
SP - 1
EP - 11
AB - We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that $\ell ^p$, $(1\le p \le \infty )$ are $Q$ algebras and that $A_n = {\frak Z}L^1({\bf Z};1+|n|^\alpha )$ is a $Q$-algebra if and only if $\alpha &gt; 1/2$.
LA - eng
UR - http://eudml.org/doc/74099
ER -

References

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  1. [1] J. WERMER, Quotient algebras of uniform algebras, Symposium on Function algebras and rational approximation, University of Michigan 1969. Zbl0176.11303
  2. [2] A. M. DAVIE, Quotient algebras of uniform algebras (to appear). Zbl0264.46055
  3. [3] L. SCHWARTZ, Séminaire 1953-1954, Produits tensoriels topologiques, Exposé n° 7 II. 
  4. [4] A. P. CALDERON, Intermediate spaces and interpolation, the complex method. Studia Math., T. xxiv (1964), 113-190. Zbl0204.13703MR29 #5097
  5. [5] N. Th. VAROPOULOS, Tensor algebras and harmonic analysis, Acta Math. 119 (1967), 51-111. Zbl0163.37002MR39 #1911
  6. [6] A. ZYGMUND, Trigonometric series, C.I.P. (1959), vol. I, ch. VI, § 3 ; vol. II, ch. XII § 8. Zbl0085.05601
  7. [7] N. Th. VAROPOULOS, Sur les quotients des algèbres uniformes, C.R. Acad. Sci. t. 274 (A) p. 1344-1346. Zbl0245.46072
  8. [8] N. Th. VAROPOULOS, Tensor algebras over discrete spaces, J. Functional Analysis, 3 (1969), 321-335. Zbl0183.14502MR40 #3328

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