A survey of recent results on the spectral radius in Banach algebras
A Note on the Raical of a Banach Algebra.
On the Gelfand-Hille theorems
Spectral radius characterization of commutativity in Banach algebras
Spectral characterization of two-sided ideals in Banach algebras
Properties of the spectral radius in Banach algebras
Geometric characteristic of semi-Fredholm operators and their asymptotic behaviour
Powers of operators
Orbits in strips
Qualitative properties of the peripheral spectrum
Nowhere dense set which is finitely open
A remark on transitivity of operator algebras
Concerning spectral characterizations of the radical in Banach algebras
A resolvent condition implying power boundedness
The Ritt and Kreiss resolvent conditions are related to the behaviour of the powers and their various means. In particular, it is shown that the Ritt condition implies the power boundedness. This improves the Nevanlinna characterization of the sublinear decay of the differences of the consecutive powers in the Esterle-Katznelson-Tzafriri theorem, and actually characterizes the analytic Ritt condition by two geometric properties of the powers.
Lower s-numbers and their asymptotic behaviour
A spectral approach to the Kaplansky problem
Quasi-nilpotent and compact
Polynomials in the Volterra and Ritt operators
We continue the paper [Ts] on the boundedness of polynomials in the Volterra operator. This provides new ways of constructing power-bounded operators. It seems interesting to point out that a similar procedure applies to the operators satisfying the Ritt resolvent condition: compare Theorem 5 and Theorem 9 below.
Continuite lipschitzienne du spectre comme fonction d'un opérateur normal
The Gerschgorin discs under unitary similarity
The intersection of the Gerschgorin regions over the unitary similarity orbit of a given matrix is studied. It reduces to the spectrum in some cases: for instance, if the matrix satisfies a quadratic equation, and also for matrices having "large" singular values or diagonal entries. This leads to a number of open questions.
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