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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.