Spaces of type H ∞ + C

Walter Rudin

Annales de l'institut Fourier (1975)

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

Abstract

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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 ∞ + C is a closed subalgebra of L ∞ . 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.

How to cite

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Rudin, 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

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