The spectral radius formula in quotient algebras

1975 ◽  
Vol 145 (2) ◽  
pp. 157-161 ◽  
Author(s):  
M. R. F. Smyth ◽  
T. T. West
Keyword(s):  
Spectral Radius ◽  
Spectral Radius Formula

scholarly journals Asymptotic stability and generalized Gelfand spectral radius formula

1997 ◽  
Vol 252 (1-3) ◽  
pp. 61-70 ◽  
Author(s):  
Mau-Hsiang Shih ◽  
Jinn-Wen Wu ◽  
Chin-Tzong Pang
Keyword(s):  
Asymptotic Stability ◽  
Spectral Radius ◽  
Spectral Radius Formula

scholarly journals The Spectral Radius Formula for Fourier–Stieltjes Algebras

2019 ◽  
Vol 63 (2) ◽  
pp. 269-275
Author(s):  
Przemysław Ohrysko ◽  
Maria Roginskaya
Keyword(s):  
Abelian Group ◽  
Spectral Radius ◽  
Haar Measure ◽  
Short Note ◽  
Measure Algebra ◽  
Stieltjes Transform ◽  
Locally Compact ◽  
Convolution Powers ◽  
Discrete Abelian Group ◽  
Spectral Radius Formula

AbstractIn this short note we first extend the validity of the spectral radius formula, obtained by M. Anoussis and G. Gatzouras, for Fourier–Stieltjes algebras. The second part is devoted to showing that, for the measure algebra on any locally compact non-discrete Abelian group, there are no non-trivial constraints among three quantities: the norm, the spectral radius, and the supremum of the Fourier–Stieltjes transform, even if we restrict our attention to measures with all convolution powers singular with respect to the Haar measure.

2.2. The spectral radius formula in quotient algebras

1984 ◽  
Vol 26 (5) ◽  
pp. 2113-2113
Author(s):  
G. J. Murphy ◽  
M. R. F. Smyth ◽  
T. T. West
Keyword(s):  
Spectral Radius ◽  
Spectral Radius Formula

scholarly journals A formula for the inner spectral radius

2004 ◽  
Vol 2004 (61) ◽  
pp. 3285-3290
Author(s):  
S. Mahmoud Manjegani
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Asymptotic Formula ◽  
Spectral Radius ◽  
Bounded Linear Operator ◽  
Bounded Linear ◽  
Spectral Radius Formula

This note presents an asymptotic formula for the minimum of the moduli of the elements in the spectrum of a bounded linear operator acting on Banach spaceX. This minimum moduli is called the inner spectral radius, and the formula established herein is an analogue of Gelfand's spectral radius formula.

On the spectral radii and principal eigenvectors of uniform hypergraphs

2017 ◽  
Vol 09 (04) ◽  
pp. 1750048 ◽  
Author(s):  
Xuelian Si ◽  
Xiying Yuan
Keyword(s):  
Spectral Radius ◽  
Lower Bounds ◽  
Uniform Hypergraph ◽  
Principal Eigenvector ◽  
Uniform Hypergraphs ◽  
Positive Eigenvector ◽  
Spectral Radius Formula

Let [Formula: see text] be a connected [Formula: see text]-uniform hypergraph. The unique positive eigenvector [Formula: see text] with [Formula: see text] corresponding to spectral radius [Formula: see text] is called the principal eigenvector of [Formula: see text]. In this paper, we present some lower bounds for the spectral radius [Formula: see text] and investigate the bounds of entries of the principal eigenvector of [Formula: see text].

Norm and spectral radius for algebraic elements of a Banach algebra

1980 ◽  
Vol 88 (1) ◽  
pp. 129-133 ◽  
Author(s):  
N. J. Young
Keyword(s):  
Banach Algebra ◽  
Spectral Radius ◽  
Upper Bound ◽  
Good Deal ◽  
Additional Information ◽  
Algebraic Element ◽  
Algebraic Elements ◽  
Image Position ◽  
Spectral Radius Formula ◽  
Unit Norm

The purpose of this note is to show that, for any algebraic element a of a Banach algebra and certain analytic functions f, one can give an upper bound for ‖f(a)‖ in terms of ‖a‖ and the spectral radius ρ(a) of a. To illustrate the nature of the result, consider the norms of powers of an element a of unit norm. In general, the spectral radius formulacontains all that can be said (that is, the limit ρ(a) can be approached arbitrarily slowly). If we have the additional information that a is algebraic of degree n we can say a good deal more. In the case of a C*-algebra we have the neat result that, if ‖a‖ ≤ 1,(see Theorem 2), while for a general Banach algebra we have at least

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