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The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.

Approximately partial ternary quadratic derivations on Banach ternary algebras.

Javadian, A., Gordji, M.Eshaghi, Savadkouhi, M.Bavand (2011)

The Journal of Nonlinear Sciences and its Applications

Automatic continuity of operational calculi on algebras of differentiable functions

Neumann, Michael (1980)

Abstracta. 8th Winter School on Abstract Analysis

Automorphism Groups of Jordan C*-Algebras.

Harald Upmeier (1981)

Mathematische Zeitschrift

Automorphisms and derivations on a universally complete complex $f$ -algebra.

Kusraev, A.G. (2006)

Sibirskij Matematicheskij Zhurnal

Banach S-algebras and conditional basic sequences in non-Montel Fréchet spaces

Steven Bellenot (1984)

Studia Mathematica

Bemerkungen über elementare Funktionen in nichtarchimedischen Banachalgebren.

Werner Blum (1974)

Manuscripta mathematica

Closed operators affiliated with a Banach algebra of operators

Bruce Barnes (1992)

Studia Mathematica

Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. If S is a closed operator in X such that (λ - S)^{-1} ∈ ℬ for some number λ, then S is affiliated with ℬ. The object of this paper is to study the spectral theory and Fredholm theory relative to ℬ of an operator which is affiliated with ℬ. Also, applications are given to semigroups of operators which are contained in ℬ.

Contributi all'analisi spettrale algebrica

Paolo Boero (1973)

Rendiconti del Seminario Matematico della Università di Padova

Convergence of vectorial continued fractions related to the spectral seminorm.

Hemdaoui, M., Amzil, M. (2008)

Journal of Inequalities and Applications [electronic only]

Convexity around the Unit of a Banach Algebra

Kadets, Vladimir, Katkova, Olga, Martín, Miguel, Vishnyakova, Anna (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.We estimate the (midpoint) modulus of convexity at the unit 1 of a Banach algebra A showing that inf {max±||1 ± x|| − 1 : x ∈ A, ||x||=ε} ≥ (π/4e)ε²+o(ε²) as ε → 0. We also give a characterization of two-dimensional subspaces of Banach algebras containing the identity in terms of polynomial inequalities.

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