Minimal superalgebras of weak- Dirichlet algebras

Author:
Takahiko Nakazi

Journal:
Proc. Amer. Math. Soc. **95** (1985), 70-72

MSC:
Primary 46J10

DOI:
https://doi.org/10.1090/S0002-9939-1985-0796448-8

MathSciNet review:
796448

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Abstract: Let be a weak- Dirichlet algebra in and let be the weak- closure of in . It may happen that there are minimal weak- closed subalgebras of that contain properly. In this paper it is shown that if there is a minimal, proper, weak- closed superalgebra of , then, in fact, that algebra is the unique least element in the lattice of all proper weak- closed superalgebras of .

**[1]**R. Kallenborn and H. König,*An invariant subspace theorem in the abstract Hardy algebra theory*, Arch. Math.**39**(1982), 51-58. MR**674533 (83m:46077)****[2]**P. S. Muhly,*Maximal weak-**Dirichlet algebras*, Proc. Amer. Math. Soc.**36**(1972), 515-518. MR**0317056 (47:5604)****[3]**T. Nakazi,*Superalgebras of weak-**Dirichlet algebras*, Pacific J. Math.**68**(1977), 197-207. MR**0500164 (58:17853)****[4]**-,*Invariant subspaces of weak-**Dirichlet algebras*, Pacific J. Math.**69**(1977), 151-167. MR**0493359 (58:12384)****[5]**-,*Quasi-maximal ideals and quasi-primary ideals of weak-**Dirichlet algebras*, J. Math. Soc. Japan**31**(1979), 677-685.**[6]**T. P. Srinivasan and J.-K. Wang,*Weak-**Dirichlet algebras*, Function Algebras, Scott, Foresman, and Co., Chicago, 1966, pp. 216-249. MR**0198282 (33:6441)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0796448-8

Keywords:
Minimal weak- closed superalgebras,
weak- Dirichlet algebra,
Hardy space,
uniform algebra

Article copyright:
© Copyright 1985
American Mathematical Society