منابع مشابه
Algebraic Perron-Frobenlus Theory
Let V be a vector space over a fully ordered field F. In Sec. 2 we characterize cones K with ascending chain condition (ACC) on faces of Ii. In Sec. 3 we show that if K has ACC on faces, then an operator A is strongly irreducible if and only if A is irreducible. In Sec. 4 we prove theorems of Perron-Frobenius type for a strongly irreducible operator A in the case that FR, the real field, and K ...
متن کاملPerron-frobenius Theory for Complex Matrices
The purpose of this paper is to present a unified Perron-Frobenius Theory for nonnegative, for real not necessarily nonnegative and for general complex matrices. The sign-real spectral radius was introduced for general real matrices. This quantity was shown to share certain properties with the Perron root of nonnegative matrices. In this paper we introduce the sign-complex spectral radius. Agai...
متن کاملMultiple Perron-Frobenius operators.
A cycle expansion technique for discrete sums of several PF operators, similar to the one used in the standard classical dynamical zeta-function formalism is constructed. It is shown that the corresponding expansion coefficients show an interesting universal behavior, which illustrates the details of the interference between the particular mappings entering the sum.
متن کاملPerron-frobenius Theory for Positive Maps on Trace Ideals
This article provides sufficient conditions for positive maps on the Schatten classes Jp; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1, the space of trace class operators, to have a unique, stric...
متن کاملPerron-frobenius Theory and the Zeros of Polynomials
1. J. Douglas, Jr. and T. M. Gallie, An approximate solution of an improper boundary value problem, Duke Math. J. vol. 26 (1959) pp. 339-347. 2. F. John, Numerical solution of the equation of heat conduction for preceding times, Ann. Mat. Pura Appl. ser. IV vol. 40 (1955) pp. 129-142. 3. C. Pucci, Sui problemi di Cauchy non "ben posti," Atti Accad. Naz. Lincei. Rend. Cl. Sei. Fis. Mat. Nat. vol...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1975
ISSN: 0024-3795
DOI: 10.1016/0024-3795(75)90022-1