# On a class of convolution algebras of functions

Annales de l'institut Fourier (1977)

- Volume: 27, Issue: 3, page 135-162
- ISSN: 0373-0956

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topFeichtinger, Hans G.. "On a class of convolution algebras of functions." Annales de l'institut Fourier 27.3 (1977): 135-162. <http://eudml.org/doc/74324>.

@article{Feichtinger1977,

abstract = {The Banach spaces $\Lambda (A,B,X,G)$ defined in this paper consist essentially of those elements of $L^1(G)$ ($G$ being a locally compact group) which can in a certain sense be well approximated by functions with compact support. The main result of this paper is the fact that in many cases $\Lambda (A,B,X,G)$ becomes a Banach convolution algebra. There exist many natural examples. Furthermore some theorems concerning inclusion results and the structure of these spaces are given. In particular we prove that simple conditions imply the existence of left approximate units or the density of $K(G)$. In the latter case a characterization of the closed left ideals is possible.},

author = {Feichtinger, Hans G.},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {3},

pages = {135-162},

publisher = {Association des Annales de l'Institut Fourier},

title = {On a class of convolution algebras of functions},

url = {http://eudml.org/doc/74324},

volume = {27},

year = {1977},

}

TY - JOUR

AU - Feichtinger, Hans G.

TI - On a class of convolution algebras of functions

JO - Annales de l'institut Fourier

PY - 1977

PB - Association des Annales de l'Institut Fourier

VL - 27

IS - 3

SP - 135

EP - 162

AB - The Banach spaces $\Lambda (A,B,X,G)$ defined in this paper consist essentially of those elements of $L^1(G)$ ($G$ being a locally compact group) which can in a certain sense be well approximated by functions with compact support. The main result of this paper is the fact that in many cases $\Lambda (A,B,X,G)$ becomes a Banach convolution algebra. There exist many natural examples. Furthermore some theorems concerning inclusion results and the structure of these spaces are given. In particular we prove that simple conditions imply the existence of left approximate units or the density of $K(G)$. In the latter case a characterization of the closed left ideals is possible.

LA - eng

UR - http://eudml.org/doc/74324

ER -

## References

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- [7] H. REITER, Classical harmonic analysis and locally compact groups, Oxford University Press, 1968. Zbl0165.15601MR46 #5933
- [8] R. SPECTOR, Sur la structure locale des groupes abéliens localement compacts, Bull. Soc. Math. France, Mémoire 24 (1970). Zbl0215.18603MR44 #729
- [9] H. CH. WANG, Nonfactorization in group algebras, Studia math., 42 (1972), 231-241. Zbl0273.43008MR46 #2355
- [10] L.H. BRANDENBURG, On identifying the maximal ideals in Banach algebras, J. Math. Anal. Appl., 50 (1975), 489-510. Zbl0302.46042MR51 #13695
- [11] I.I. HIRSCHMANN, Finite sections of Wiener-Hopf equations and Szegö polynomials, J. Math. Anal. Appl., 11 (1965), 290-320. Zbl0173.42601MR31 #6133

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