Factorisation without bounded approximate identities

J. Ward

Colloquium Mathematicae (1992)

  • Volume: 63, Issue: 2, page 273-284
  • ISSN: 0010-1354

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Ward, J.. "Factorisation without bounded approximate identities." Colloquium Mathematicae 63.2 (1992): 273-284. <http://eudml.org/doc/210152>.

@article{Ward1992,
author = {Ward, J.},
journal = {Colloquium Mathematicae},
keywords = {bounded approximate identity; Banach algebra; normed space; pseudomeasure spaces; compact abelian group; convolution multiplication; Fourier transform; non locally convex metric space; convolution algebra with factorization},
language = {eng},
number = {2},
pages = {273-284},
title = {Factorisation without bounded approximate identities},
url = {http://eudml.org/doc/210152},
volume = {63},
year = {1992},
}

TY - JOUR
AU - Ward, J.
TI - Factorisation without bounded approximate identities
JO - Colloquium Mathematicae
PY - 1992
VL - 63
IS - 2
SP - 273
EP - 284
LA - eng
KW - bounded approximate identity; Banach algebra; normed space; pseudomeasure spaces; compact abelian group; convolution multiplication; Fourier transform; non locally convex metric space; convolution algebra with factorization
UR - http://eudml.org/doc/210152
ER -

References

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  2. [2] P. C. Curtis Jr. and A. Figà-Talamanca, Factorization theorems for Banach algebras, in: Function Algebras, Scott, Foresman and Co., Chicago 1966, 169-185. 
  3. [3] P. G. Dixon, Factorization and unbounded approximate identities in Banach algebras, Math. Proc. Cambridge Philos. Soc. 107 (1990), 557-571. Zbl0723.46034
  4. [4] R. E. Edwards, Lipschitz conditions and lacunarity, J. Austral. Math. Soc. 16 (1973), 272-277. 
  5. [5] R. E. Edwards, Fourier Series: a Modern Introduction, I, II, 2nd ed., Springer, New York 1979, 1982. Zbl0424.42001
  6. [6] H. G. Feichtinger and M. Leinert, Individual factorization in Banach modules, Colloq. Math. 51 (1987), 107-117. Zbl0628.46051
  7. [7] E. Hewitt, The ranges of certain convolution operators, Math. Scand. 15 (1964), 147-155. Zbl0135.36002
  8. [8] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, I, II, Springer, Berlin 1963, 1970. Zbl0115.10603
  9. [9] Y. Katznelson, An Introduction to Harmonic Analysis, Wiley, New York 1968. 
  10. [10] S. M. Khaleelulla, Counterexamples in Topological Vector Spaces, Lecture Notes in Math. 936, Springer, Berlin 1982. Zbl0482.46002
  11. [11] E. Kreysig, Introductory Functional Analysis with Applications, Wiley, New York 1978. 
  12. [12] W. Rudin, Factorization in the group algebra of the real line, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 339-340. Zbl0079.13301
  13. [13] W. Rudin, Representaion of functions by convolutions, J. Math. Mech. 7 (1958), 103-115. Zbl0079.13302
  14. [14] S. Saeki, The L p -conjecture and Young’s inequality, Illinois J. Math. 34 (1990), 614-627. Zbl0701.22003
  15. [15] R. Salem, Sur les transformations des séries de Fourier, Fund. Math. 33 (1945), 108-114. Zbl65.1203.01
  16. [16] H. C. Wang, Homogeneous Banach Algebras, Marcel Dekker, New York 1977. 
  17. [17] A. Wilansky, Functional Analysis, Blaisdell, New York 1964. Zbl0136.10603
  18. [18] G. Willis, Examples of factorisation without bounded approximate identities, preprint, 1989. 

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