Douglas algebras without maximal subalgebra and without minimal superalgebra.
Guillory, Carroll (2001)
Abstract and Applied Analysis
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Guillory, Carroll (2001)
Abstract and Applied Analysis
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H. Länger (1978)
Fundamenta Mathematicae
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Iulian Popovici, Radu Iordanescu, Adriana Turtoi (1971)
Archivum Mathematicum
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Philip Nanzetta (1968)
Fundamenta Mathematicae
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Frank Terpe (1971)
Colloquium Mathematicae
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J. W. Bebernes, Steven K. Ingram (1971)
Annales Polonici Mathematici
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M. A. Selby (1974)
Colloquium Mathematicae
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Pamela Gorkin, Anthony G. O'Farrell (2011)
Studia Mathematica
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A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X). It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain...
Ralph K. Amayo (1975)
Compositio Mathematica
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Doroslovački, Rade, Pantović, Jovanka, Vojvodić, Gradimir (1999)
Novi Sad Journal of Mathematics
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A. M. Stokolos (2006)
Colloquium Mathematicae
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The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.