Proceedings of the American Mathematical Society

Weak spectral synthesis for the projective tensor product of commutative Banach algebras

Author(s): Eberhard Kaniuth
Journal: Proc. Amer. Math. Soc. 132 (2004), 2959-2967.
MSC (2000): Primary 46J20, 46J05
Posted: June 2, 2004
Retrieve article in: PDF DVI PostScript

Abstract: Let

and

be regular commutative Banach algebras and $A \widehat{\otimes} B$ their projective tensor product, and suppose that $A \widehat{\otimes} B$ is semisimple. We investigate the relation between weak spectral synthesis properties of $A \widehat{\otimes} B$ and those of

and

1.: A. Atzmon, Spectral synthesis in regular Banach algebras, Israel J. Math. 8 (1970), 197-212. MR 41:8932
2.: W. Badé and P.C. Curtis, Jr., The Wedderburn decomposition of commutative Banach algebras, Amer. J. Math. 82 (1960), 851-866. MR 23:A529
3.: P. Enflo, A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309-317. MR 53:6288
4.: B.R. Gelbaum, Tensor products of Banach algebras, Canad. J. Math. 11 (1959), 297-310. MR 21:2922
5.: W. Kirsch and D. Müller, On the synthesis problem for orbits of Lie groups in $\mathbb{R} ^n$ , Ark. Mat. 18 (1980), 145-155. MR 82f:43006
6.: R. Larsen, Banach algebras, Marcel Dekker, New York, 1973. MR 58:7010
7.: H. Milne, Banach space properties of uniform algebras, Bull. London Math. Soc. 4 (1972), 323-326. MR 48:847
8.: K. Parthasarathy and S. Varma, On weak spectral synthesis, Bull. Austral. Math. Soc. 43 (1991), 279-282. MR 92d:43007
9.: C.E. Rickart, General theory of Banach algebras, D. van Nostrand, 1960. MR 22:5903
10.: G.E. Shilov, On regular normed rings, Trav. Inst. Math. Steklov (Moscow) 21 (1947), 118 pp. (Russian. English summary). MR 9:596a
11.: J. Tomiyama, Tensor products of commutative Banach algebras, Tohoku Math. J. (2) 12 (1960), 147-154. MR 22:5910
12.: N.Th. Varopoulos, Spectral synthesis on spheres, Proc. Cambridge Philos. Soc. 62 (1966), 379-387. MR 34:1786
13.: N.Th. Varopoulos, Tensor algebras and harmonic analysis, Acta Math. 119 (1967), 51-111. MR 39:1911
14.: C.R. Warner, Weak spectral synthesis, Proc. Amer. Math. Soc. 99 (1987), 244-248. MR 88c:43005
15.: C.R. Warner, Spectral synthesis in the Mirkil algebra, J. Math. Anal. Appl. 167 (1992), 176-181. MR 93i:46092

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46J20, 46J05

Eberhard Kaniuth
Affiliation: Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany
Email: kaniuth@math.uni-paderborn.de

DOI: 10.1090/S0002-9939-04-07579-3
PII: S 0002-9939(04)07579-3
Received by editor(s): February 3, 2003
Posted: June 2, 2004
Communicated by: David R. Larson
Copyright of article: Copyright 2004, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS