A Uniform Algebra of Analytic Functions on a Banach Space

DOI10.2307/2001402zbMath0704.46033OpenAlexW4229840993MaRDI QIDQ3483853

T. K. Carne, Brian J. Cole, Theodore W. Gamelin

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001402

zbMATH Keywords

Schur propertyDunford-Pettis propertytightnessuniform algebrametric approximation propertyalgebra of bounded analytic functionsweak polynomial topologyHankel-type operator\(\Lambda \) -space

Mathematics Subject Classification ID

Banach algebras of continuous functions, function algebras (46J10) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Radon-Nikodým, Kre?n-Milman and related properties (46B22) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (27)

Polynomial topologies on Banach spaces ⋮ Polynomial reflexivity in Banach spaces ⋮ Upper l_p-estimates in vector sequence spaces, with some applications ⋮ Fredholm composition operators on algebras of analytic functions on Banach spaces ⋮ \(L\)-sets and property \((SR^*)\) in spaces of compact operators ⋮ A class of sets in a Banach space coarser than limited sets ⋮ A Theorem on Polynomial-Star Approximation ⋮ Polynomially continuous operators ⋮ On geometric extension of polynomials on Banach spaces ⋮ Hardy type spaces associated with compact unitary groups ⋮ Absolutely \((r,q)\)-summing operators on vector-valued function spaces ⋮ Bishop's theorem and differentiability of a subspace of \(C_b(K)\) ⋮ Complete latticeability in vector‐valued sequence spaces ⋮ Polynomial sequential continuity on \(C(K,E)\) spaces ⋮ The \(w_{EF}\) topology for a Banach space \(E\) ⋮ Weak-Polynomial Convergence on a Banach Space ⋮ Estimates by polynomials ⋮ Polynomial continuity on $\ell _1$ ⋮ Interpolating sequences for weighted spaces of analytic functions on the unit ball of a Hilbert space ⋮ Unique Hahn-Banach theorems for spaces of homogeneous polynomials ⋮ Two-sided polynomial ideals on Banach spaces ⋮ Weak-polynomial convergence on spaces \(\ell_{p}\) and \(L_{p}\) ⋮ A Semiring in the Spectrum of the Algebra of Symmetric Analytic Functions in the Space ℓ1 ⋮ Polynomial compactness in Banach spaces ⋮ The positive polynomial Schur property in Banach lattices ⋮ Bloch functions on the unit ball of a Banach space ⋮ Connected components in the space of composition operators on \(H^\infty\) functions of many variables

Cites Work

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• Weak-star continuous homomorphisms and a decomposition of orthogonal measures
• Tight uniform algebras and algebras of analytic functions
• A property of multilinear operations
• The Equation L(E, X ∗ ∗ = L(E, X) ∗ ∗ and the Principle of Local Reflexivity
• A Note on Bilinear Forms

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