A formula for the joint local spectral radius

Emel'yanov, EY
Ercan, Z
We give a formula for the joint local spectral radius of a bounded subset of bounded linear operators on a Banach space X in terms of the dual of X.


Concrete description of CD0(K)-spaces as C(X)-spaces and its applications
Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
An abstract approach to Bohr's phenomenon
Aizenberg, L; Aytuna, A; Djakov, P (American Mathematical Society (AMS), 2000-01-01)
In 1914 Bohr discovered that there exists r is an element of (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1, then for \z\ < r the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. Our aim here is to present an abstract approach to the problem and show that Bohr's phenomenon occurs under very general conditions.
A classification of equivariant principal bundles over nonsingular toric varieties
Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2016-12-01)
We classify holomorphic as well as algebraic torus equivariant principal G-bundles over a nonsingular toric variety X, where G is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.
Manguoğlu, Murat (Society for Industrial & Applied Mathematics (SIAM), 2019-01-01)
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with a relatively small number of negative eigenvalues. The proposed scheme consists of an outer minimum residual (MINRES) iteration, preconditioned by an inner conjugate gradient (CG) iteration in which CG can be further preconditioned. The robustness of the proposed scheme is illustrated by solving indefinite linear systems that arise in t...
An alternative series solution to the isotropic quartic oscillator in N dimensions
Taşeli, Hasan (Springer Science and Business Media LLC, 1996-01-01)
The series solution of the N-dimensional isotropic quartic oscillator weighted by an appropriate function which exhibits the correct asymptotic behavior of the wave function is presented. The numerical performance of the solution in Bill's determinant picture is excellent, and yields the energy spectrum of the system to any desired accuracy for the full range of the coupling constant. Furthermore, it converges to the well-known exact solution of the unperturbed harmonic oscillator wave function, when the an...
Citation Formats
E. Emel’yanov and Z. Ercan, “A formula for the joint local spectral radius,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 1449–1451, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65280.