Projections onto translation-invariant subspaces of 𝐿₁(𝑅)

Alspach, Dale E.; Matheson, Alec

doi:10.1090/S0002-9947-1983-0694390-7

Projections onto translation-invariant subspaces of $L_{1}(\textbf {R})$
HTML articles powered by AMS MathViewer

by Dale E. Alspach and Alec Matheson

Trans. Amer. Math. Soc. 277 (1983), 815-823

DOI: https://doi.org/10.1090/S0002-9947-1983-0694390-7

PDF | Request permission

Abstract:

The complemented translation-invariant subspaces of ${L_1}({\mathbf {R}})$ are characterized. This completes an investigation begun by H. P. Rosenthal.

References

J. Bourgain, A new class of ${\cal L}^{1}$-spaces, Israel J. Math. 39 (1981), no. 1-2, 113–126. MR 617294, DOI 10.1007/BF02762857
John E. Gilbert, On a strong form of spectral synthesis, Ark. Mat. 7 (1969), 571–575. MR 278008, DOI 10.1007/BF02590895
John E. Gilbert, On projections of $L^{\infty }(G)$ onto translation-invariant subspaces, Proc. London Math. Soc. (3) 19 (1969), 69–88. MR 244705, DOI 10.1112/plms/s3-19.1.69

Some geometrical properties of Banach spaces of polynomials

W. B. Johnson and J. Lindenstrauss, Examples of ${\cal L}_{1}$ spaces, Ark. Mat. 18 (1980), no. 1, 101–106. MR 608329, DOI 10.1007/BF02384683
Jean-Pierre Kahane, Sur les polynômes à coefficients unimodulaires, Bull. London Math. Soc. 12 (1980), no. 5, 321–342 (French). MR 587702, DOI 10.1112/blms/12.5.321
Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 0422992
Joram Lindenstrauss, A remark on ${\cal L}_{1}$ spaces, Israel J. Math. 8 (1970), 80–82. MR 259582, DOI 10.1007/BF02771554
J. Lindenstrauss, On a certain subspace of $l_{1}$, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12 (1964), 539–542. MR 174963
J. Lindenstrauss and H. P. Rosenthal, The ${\cal L}_{p}$ spaces, Israel J. Math. 7 (1969), 325–349. MR 270119, DOI 10.1007/BF02788865
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8
Teng-Sun Liu, Arnoud van Rooij, and Ju Kwei Wang, Projections and approximate identities for ideals in group algebras, Trans. Amer. Math. Soc. 175 (1973), 469–482. MR 318781, DOI 10.1090/S0002-9947-1973-0318781-2
Haskell P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13–36. MR 270122, DOI 10.4064/sm-37-1-13-36
Haskell P. Rosenthal, On the existence of approximate identities in ideals of group algebras, Ark. Mat. 7 (1967), 185–191 (1967). MR 239362, DOI 10.1007/BF02591035
Haskell P. Rosenthal, Projections onto translation-invariant subspaces of $L^{p}(G)$, Mem. Amer. Math. Soc. 63 (1966), 84. MR 211198
Sadahiro Saeki, On strong Ditkin sets, Ark. Mat. 10 (1972), 1–7. MR 310554, DOI 10.1007/BF02384797
Bert M. Schreiber, On the coset ring and strong Ditkin sets, Pacific J. Math. 32 (1970), 805–812. MR 259502, DOI 10.2140/pjm.1970.32.805