Maximal subalgebra of Douglas algebra.
m-convexité dans le corps C(X).
Multipliers and hereditary subalgebras of operator algebras
We generalize some technical results of Glicksberg to the realm of general operator algebras and use them to give a characterization of open and closed projections in terms of certain multiplier algebras. This generalizes a theorem of J. Wells characterizing an important class of ideals in uniform algebras. The difficult implication in our main theorem is that if a projection is open in an operator algebra, then the multiplier algebra of the associated hereditary subalgebra arises as the closure...
Normed "upper interval" algebras without nontrivial closed subalgebras
It is a long standing open problem whether there is any infinite-dimensional commutative Banach algebra without nontrivial closed ideals. This is in some sense the Banach algebraists' counterpart to the invariant subspace problem for Banach spaces. We do not here solve this famous problem, but solve a related problem, that of finding (necessarily commutative) infinite-dimensional normed algebras which do not even have nontrivial closed subalgebras. Our examples are incomplete normed algebras rather...
On dense ideals of C*-algebras and generalizations of the Gelfand-Naimark Theorem
We develop the theory of Segal algebras of commutative C*-algebras, with an emphasis on the functional representation. Our main results extend the Gelfand-Naimark Theorem. As an application, we describe faithful principal ideals of C*-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.
On domination and extensions of Banach algebras
Problèmes de complémentation de sous-algèbres dans l'algèbre des séries de Fourier en deux variables absolument convergentes
Sizes of quotient spaces of certain function algebras on topological semigroups
The Bourgain algebra of the disk algebra A(𝔻) and the algebra QA
It is shown that the Bourgain algebra of the disk algebra A() with respect to is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is .
The inverse spectral radius formula and removability of spectrum
The strong spectral extension property does not imply the multiplicative Hahn-Banach property
An example is given of a semisimple commutative Banach algebra that has the strong spectral extension property but fails the multiplicative Hahn-Banach property. This answers a question posed by M. J. Meyer in [4].
The Uniform Algebra Generated by z and a Smooth Even Function.
Uniform algebras satisfying certain extension properties
w*-closed subalgebras of
Асимптотическое поведение коэффициентов функций от степенных рядов и рядов Фурье.
Инвариантные пространства и алгебры функций на группе Гейзенберга.
Конструктивное доказательство теоремы Маршалла-Чанг
Максимальность инвариантных алгебр функций
О максимальности алгебры функций, непрерывных на расширенной комплексной плоскости и аналитических в дополнении к вполне разрывному компакту
Об антисимметричных алгебрах дифференцируемых функций на гладких многообразиях