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References
A. Beurling, On two problems concerning linear transformations in Hilbert space. Acta Math. 81(1949), 239–255.
M. M. Day, The spaces LP with 0<p<1. Bull. Amer. Math. Soc. 46(1940), 816–823.
P. L. Duren, Theory of HP Spaces. Academic Press, New York, 1970.
_____, Smoothness of functions generated by Riesz products. Proc. Amer. Math. Soc. 16(1965), 1263–1268.
P. L. Duren, B. W. Romberg, and A. L. Shileds, Linear functionals on HP spaces with 0<p<1. J. reine angew. Math. 238(1969), 32–60.
T. W. Gamelin, Uniform Algebras. Prentice Hall, Englewood Cliffs, N.J. 1969.
D. A. Gregory and J. H. Shapiro, Nonconvex linear topologies with the Hahn-Banach extension property. Proc. Amer. Math. Soc. 25(1970), 902–905.
G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals II. Math. Z. 34(1932), 403–439.
P. Hartman and R. Kershner, The structure of monotone functions. Amer. J. Math. 59(1937), 809–822.
H. Helson, Lectures on Invariant Subspaces. Academic Press, New York, 1964.
K. Hoffman, Banach Spaces of Analytic Functions. Prentice-Hall, Englewood Dliffs, N.J. 1962.
N. J. Kalton, Basic sequences in F-sapces and their applications. Proc. Edinburgh Math. Soc. (2)19(1974), 151–167.
_____, Compact and strictly singular operators on Orlicz spaces. Israel J. Math. (to appear).
N. J. Kalton and J. H. Shapiro, An F-space with trivial dual and non-trivial compact endomorphisms. Israel J. Math. 20(1975), 282–291.
J. L. Kelley, I. Namioka, et al., Linear Topological Spaces, Van Nostrand, Princeton, 1963.
E. Landau, Darstellung und Begrundung einiger neurer Ergebnisse der Funktiontheorie. Springer, Berlin, 1929.
A. E. Livingston, The space HP, 0<p<1, is not normable. Pacific J. Math. 3(1953), 613–616.
D. Pallaschkte, The compact endomorphisms of the metric linear space φ. Studia Math. 47(1973), 153–165.
J. W. Roberts, A compact convex set with no extreme points. Studia Math., to appear.
_____, In preparation.
J. W. Roberts and M. Stoll, Prime and principal ideals in the algebra N+. Arkiv der Matematik, 27(1976), 387–393.
W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
H. S. Shapiro, Weakly invertible elements in certain function spaces, and generators in ℓ1. Michigan Math. J. 11(1964), 161–165.
_____, A class of singular functions. Canad. J. Math. 20(1968), 1425–1431.
_____, Some remarks on weighted polynomial approximation of holomorphic functions. Mat. Sbornik 73(1967), 320–330 (in Russian).
_____, Weighted polynomial approximation and boundary behavior of holomorphic functions. In the volume "Contemporary Investigations in the Theory of Functions", Nauka, Moscow, 1966, 326–335.
J. H. Shapiro, Examples of proper, closed, weakly dense subspaces in some F-spaces of analytic functions. Israel J. Math. 7(1969), 369–380.
_____, Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Bergman spaces. Duke Math. J. 43(1976), 187–202.
J. H. Shapiro and A. L. Shields, Unusual topological properties of the Nevanlinna Class. Amer. J. Math. 97(1976), 915–936.
W. J. Stiles, On properties of subspaces of ℓp, 0<p<1. Trans. Amer. Math. Soc. 149(1970), 405–415.
N. Yanigahara, The containing Fréchet space for the class N+. Duke Math. J. 40(1973), 93–103.
_____, Multipliers and linear functionals for the class N+. Trans. Amer. Math. Soc. 180(1973), 449–461.
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Shapiro, J.H. (1977). Remarks on F-spaces of analytic functions. In: Baker, J., Cleaver, C., Diestel, J. (eds) Banach Spaces of Analytic Functions. Lecture Notes in Mathematics, vol 604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069213
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DOI: https://doi.org/10.1007/BFb0069213
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