A remark to a theorem of Yu. A. Abramovich

A remarkable theorem due to Abramovich (1988) states that any surjective positive isometry on a Banach lattice has a positive inverse. In this note we discuss a renorming problem for Banach lattices and show that the theorem cannot be generalized to the case of the doubly power bounded positive operators.


The period-index problem of the canonical gerbe of symplectic and orthogonal bundles
BİSWAS, Indranil; Coşkun, Emre; DHİLLON, Ajneet (2016-01-15)
We consider regularly stable parabolic symplectic and orthogonal bundles over an irreducible smooth projective curve over an algebraically closed field of characteristic zero. The morphism from the moduli stack of such bundles to its coarse moduli space is a mu(2)-gerbe. We study the period and index of this gerbe, and solve the corresponding period-index problem.
A Fourier-Bessel expansion for solving radial Schrodinger equation in two dimensions
Taşeli, Hasan (Wiley, 1997-02-15)
The spectrum of the two-dimensional Schrodinger equation for polynomial oscillators bounded by infinitely high potentials, where the eigenvalue problem is defined on a finite interval r is an element of [0, L), is variationally studied. The wave function is expanded into a Fourier-Bessel series, and matrix elements in terms of integrals involving Bessel functions are evaluated analytically. Numerical results presented accurate to 30 digits show that, by the time L approaches a critical value, the tow-lying ...
Asymptotic Behavior of Lotz-Rabiger and Martingale Nets
Emelyanov, Eduard (2010-09-01)
Using Theorem 1 (of convergence) in [1], we prove several results on LR- and M-nets by a unified approach to these nets that appear as the two extreme types of asymptotically abelian nets.
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...
A note on a theorem of Dwyer and Wilkerson
Öztürk, Semra (Springer Science and Business Media LLC, 2001-01-03)
We prove a version of Theorem 2.3 in [1] for the non-elementary abelian group Z(2) x Z(2n), n greater than or equal to 2. Roughly, we describe the equivariant cohomology of (union of) fixed point sets as the unstable part of the equivariant cohomology of the space localized with respect to suitable elements of the cohomology ring of Z(2) x Z(2n).
Citation Formats
E. Emelyanov, “A remark to a theorem of Yu. A. Abramovich,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 132, no. 3, pp. 781–782, 2004, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94925.