# Spaces of type ${H}^{\infty}+C$

Annales de l'institut Fourier (1975)

- Volume: 25, Issue: 1, page 99-125
- ISSN: 0373-0956

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topRudin, Walter. "Spaces of type $H^\infty +C$." Annales de l'institut Fourier 25.1 (1975): 99-125. <http://eudml.org/doc/74216>.

@article{Rudin1975,

abstract = {A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that $H^\infty +C$ is a closed subalgebra of $L^\infty $. In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.},

author = {Rudin, Walter},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {1},

pages = {99-125},

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

title = {Spaces of type $H^\infty +C$},

url = {http://eudml.org/doc/74216},

volume = {25},

year = {1975},

}

TY - JOUR

AU - Rudin, Walter

TI - Spaces of type $H^\infty +C$

JO - Annales de l'institut Fourier

PY - 1975

PB - Association des Annales de l'Institut Fourier

VL - 25

IS - 1

SP - 99

EP - 125

AB - A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that $H^\infty +C$ is a closed subalgebra of $L^\infty $. In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.

LA - eng

UR - http://eudml.org/doc/74216

ER -

## References

top- [1] L. BUNGART, Boundary kernel functions for domains on complex manifolds, Pacific J. Math., 14 (1960), 1151-1164. Zbl0144.08001MR30 #4976
- [2] F. COMBES, Sur les faces d'une C*-algèbre, Bull. Sci. Math., 93 (1969), 37-62. Zbl0177.17801MR42 #856
- [3] A.M. DAVIE, T.W. GAMELIN, and J. GARNETT, Distance estimates and pointwise bounded density, Trans. Amer. Math. Soc., 175 (1973), 37-68. Zbl0263.30033MR47 #2068
- [4] A. DEVINATZ, An extension of a limit theorem of G. Szegö, J. Math. Anal. Appl., 14 (1966), 499-510. Zbl0139.07301MR33 #7792
- [5] J. DIXMIER, Les C*-algèbres et leurs Représentations, Gauthier-Villars, Paris, 1969. Zbl0174.18601MR39 #7442
- [6] F. FORELLI, Measures whose Poisson integrals are pluriharmonic, Illinois J. Math., 18 (1974), 373-388. Zbl0296.31014MR49 #7468
- [7] H. HELSON and D. LOWDENSLAGER, Prediction theory and Fourier series in several variables, Acta Math., 99 (1958), 165-202. Zbl0082.28201MR20 #4155
- [8] H. HELSON and D. SARASON, Past and future, Math. Scand., 21 (1967), 5-16. Zbl0241.60029MR38 #5282
- [9] G.M. HENKIN, Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications, Math. USSR Sbornik, 7 (1969), 597-616. (Mat. Sbornik 78 (1969)). Zbl0208.35102
- [10] E. HEWITT and K.A. ROSS, Abstract Harmonic Analysis, Springer Verlag, Berlin ; Vol. 1, 1963 ; Vol. 2, 1970. Zbl0115.10603
- [11] A. KORANYI, Harmonic functions on hermitian hyperbolic space, Trans. Amer. Math. Soc., 135 (1969), 507-516. Zbl0174.38801MR43 #3480
- [12] A. KORANYI and S. VAGI, Singular integrals in homogeneous spaces and some problems of classical analysis, Ann. Scuola Normale Superiore Pisa, 25 (1971), 575-648. Zbl0291.43014MR57 #3462
- [13] J.T. MARTI, Introduction to the Theory of Bases, Springer Verlag, 1969. Zbl0191.41301MR55 #10994
- [14] C.E. RICKART, General Theory of Banach Algebras, Van Nostrand, 1960. Zbl0095.09702MR22 #5903
- [15] W. RUDIN, The closed ideals in an algebra of analytic functions, Can. J. Math., 9 (1957), 426-434. Zbl0080.31703MR19,641c
- [16] W. RUDIN, Fourier Analysis on Groups, Interscience, 1962. Zbl0107.09603MR27 #2808
- [17] W. RUDIN, Function Theory in Polydiscs, Benjamin, 1969. Zbl0177.34101MR41 #501
- [18] D. SARASON, Generalized interpolation in H∞, Trans. Amer. Math. Soc., 127 (1967), 179-203. Zbl0145.39303MR34 #8193
- [19] D. SARASON, Algebras of functions on the unit circle, Bull. Amer, Math. Soc., 79 (1973), 286-299. Zbl0257.46079MR48 #2777
- [20] E.M. STEIN, Boundary Behavior of Holomorphic Functions of Several Complex Variables, Princeton University Press, 1972. Zbl0242.32005MR57 #12890
- [21] E.L. STOUT, On the multiplicative Cousin problem with bounded data, Ann. Scuola Normale Superiore Pisa, 27 (1973), 1-17. Zbl0261.32008MR51 #3524
- [22] J. WICHMANN, Bounded approximate units and bounded approximate identities, Proc. Amer. Math. Soc., 41 (1973), 547-550. Zbl0272.46028MR48 #2767
- [23] L. ZALCMAN, Bounded analytic functions on domains of infinite connectivity, Trans. Amer. Math. Soc., 144 (1969), 241-269. Zbl0188.45002MR40 #5884
- [24] A. ZYGMUND, Sur un théorème de M. Fekete, Bull. Acad. Polonaise, (1927), 343-347. JFM53.0256.02
- [25] A. ZYGMUND, Trigonometric Series, 2nd Ed., Cambridge University Press, 1959. Zbl0085.05601

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