The generalized spectral-radius theorem: An analytic-geometric proof

Elsner L (1995)
Linear Algebra and its Applications 220: 151-159.

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Konferenzbeitrag | Veröffentlicht | Englisch
Abstract / Bemerkung
Let Sigma be a bounded set of complex matrices, Sigma(m) = {A(1)...A(m) : A(i) is an element of Sigma}. The generalized spectral-radius theorem states that rho(Sigma)= <(rho)over cap>(Sigma), where rho(Sigma) and <(rho)over cap>(sigma) are defined as follows: rho(Sigma) = lim sup rho(m)(Sigma){1/m}, where rho(m)(Sigma) = sup {rho(A) : A is an element of Sigma(m)} with rho (A) the spectral radius; <(rho)over cap>(Sigma) = lim sup <(rho)over cap>(m)(Sigma){1/m}, where <(rho)over cap>(m)(Sigma) = sup {parallel to A parallel to: A is an element of Sigma(m)} with parallel to parallel to any matrix norm. We give an elementary proof, based on analytic and geometric tools, which is in some ways simpler than the first proof by Berger and Wang.
Erscheinungsjahr
Band
220
Seite(n)
151-159
Konferenz
International Workshop on Nonnegative Matrices, Applications and Generalizations and 8th Haifa Matrix Theory Conference
Konferenzort
Haifa, Israel
Konferenzdatum
1993-05-31 – 1993-06-10
ISSN
PUB-ID

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Elsner L. The generalized spectral-radius theorem: An analytic-geometric proof. Linear Algebra and its Applications. 1995;220:151-159.
Elsner, L. (1995). The generalized spectral-radius theorem: An analytic-geometric proof. Linear Algebra and its Applications, 220, 151-159. doi:10.1016/0024-3795(93)00320-Y
Elsner, L. (1995). The generalized spectral-radius theorem: An analytic-geometric proof. Linear Algebra and its Applications 220, 151-159.
Elsner, L., 1995. The generalized spectral-radius theorem: An analytic-geometric proof. Linear Algebra and its Applications, 220, p 151-159.
L. Elsner, “The generalized spectral-radius theorem: An analytic-geometric proof”, Linear Algebra and its Applications, vol. 220, 1995, pp. 151-159.
Elsner, L.: The generalized spectral-radius theorem: An analytic-geometric proof. Linear Algebra and its Applications. 220, 151-159 (1995).
Elsner, Ludwig. “The generalized spectral-radius theorem: An analytic-geometric proof”. Linear Algebra and its Applications 220 (1995): 151-159.