Complemented copies of $c_ 0$ in vector valued Hardy spaces
HTML articles powered by AMS MathViewer
- by Patrick N. Dowling PDF
- Proc. Amer. Math. Soc. 107 (1989), 251-254 Request permission
Abstract:
Let $X$ be a complex Banach space containing a copy of ${c_0}$, let $\mathbb {T}$ be the unit circle and let $D$ be the open unit disk in the complex plane. Then ${H^p}(\mathbb {T},X)$ contains a complemented copy of ${c_0}$ for $1 \leq p < \infty$. The corresponding result for ${H^p}(D,X)$ fails for $1 \leq p \leq \infty$.References
- C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI 10.4064/sm-17-2-151-164
- Pilar Cembranos, $C(K,\,E)$ contains a complemented copy of $c_{0}$, Proc. Amer. Math. Soc. 91 (1984), no. 4, 556–558. MR 746089, DOI 10.1090/S0002-9939-1984-0746089-2
- J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
- Patrick N. Dowling, Duality in some vector-valued function spaces, Rocky Mountain J. Math. 22 (1992), no. 2, 511–518. MR 1180716, DOI 10.1216/rmjm/1181072745
- G. Emmanuele, On complemented copies of $c_0$ in $L^p_X,\;1\leq p<\infty$, Proc. Amer. Math. Soc. 104 (1988), no. 3, 785–786. MR 930250, DOI 10.1090/S0002-9939-1988-0930250-1
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773 E. Saab and P. Saab, On complemented copies of ${c_0}$ in injective tensor products, Contemp. Math. 52, Amer. Math. Soc. 1986.
- Andrew Sobczyk, Projection of the space $(m)$ on its subspace $(c_0)$, Bull. Amer. Math. Soc. 47 (1941), 938–947. MR 5777, DOI 10.1090/S0002-9904-1941-07593-2
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 251-254
- MSC: Primary 46E40; Secondary 46B25, 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1989-0984786-9
- MathSciNet review: 984786