scholarly journals New Results on Soft Spectral in Soft Banach Algebra

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Noori F. Al-Mayahi ◽  
Hayder K. Mohammed
Keyword(s):  
Banach Algebra ◽  
Spectral Radius ◽  
Division Algebra ◽  
Maximal Ideals ◽  
Spectral Radius Formula

 In this paper, concepts of soft character, soft division algebra, soft ideal, soft maximal ideals are introduced .Soft Spectral Radius Formula are introduced and proved, some properties of Soft gelfand algebra are proved.

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

scholarly journals 2-normed algebras-II

2011 ◽  
Vol 90 (104) ◽  
pp. 135-143
Author(s):  
Neeraj Srivastava ◽  
S. Bhattacharya ◽  
S.N. Lal
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Spectral Radius ◽  
Banach Algebras ◽  
Basic Properties ◽  
Definition Of ◽  
Spectral Radius Formula

In the first part of the paper [5], we gave a new definition of real or complex 2-normed algebras and 2-Banach algebras. Here we give two examples which establish that not all 2-normed algebras are normable and a 2-Banach algebra need not be a 2-Banach space. We conclude by deriving a new and interesting spectral radius formula for 1-Banach algebras from the basic properties of 2-Banach algebras and thus vindicating our definitions of 2-normed and 2-Banach algebras given in [5].

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

Amalgamated duplication of the Banach algebra 𝔄 along a 𝔄-bimodule 𝒜

2018 ◽  
Vol 17 (09) ◽  
pp. 1850169 ◽  
Author(s):  
Hossein Javanshiri ◽  
Mehdi Nemati
Keyword(s):  
Banach Algebra ◽  
Cohomology Group ◽  
Banach Algebras ◽  
Multiplier Algebra ◽  
Topological Center ◽  
Maximal Ideals ◽  
Open Questions ◽  
Arens Regularity ◽  
Amalgamated Duplication

Let [Formula: see text] and [Formula: see text] be Banach algebras such that [Formula: see text] is a Banach [Formula: see text]-bimodule with compatible actions. We define the product [Formula: see text], which is a strongly splitting Banach algebra extension of [Formula: see text] by [Formula: see text]. After characterization of the multiplier algebra, topological center, (maximal) ideals and spectrum of [Formula: see text], we restrict our investigation to the study of semisimplicity, regularity, Arens regularity of [Formula: see text] in relation to that of the algebras [Formula: see text], [Formula: see text] and the action of [Formula: see text] on [Formula: see text]. We also compute the first cohomology group [Formula: see text] for all [Formula: see text] as well as the first-order cyclic cohomology group [Formula: see text], where [Formula: see text] is the [Formula: see text]th dual space of [Formula: see text] when [Formula: see text] and [Formula: see text] itself when [Formula: see text]. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for Lau products and module extensions of Banach algebras as well as triangular Banach algebra. Finally, special attention is devoted to the cyclic and [Formula: see text]-weak amenability of [Formula: see text]. In this context, several open questions arise.

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 Banach algebra elements whose spectra intersect R+

1974 ◽  
Vol 19 (1) ◽  
pp. 59-69 ◽  
Author(s):  
F. F. Bonsall ◽  
A. C. Thompson
Keyword(s):  
Banach Algebra ◽  
Spectral Radius ◽  
Real Numbers ◽  
Complex Banach Algebra ◽  
Image Position ◽  
Invertible Elements

Let A denote a complex Banach algebra with unit, Inv(A) the set of invertible elements of A, Sp(a) and r(a) the spectrum and spectral radius respectively of an element a of A. Let Γ denote the set of elements of A whose spectra contain non-negative real numbers, i.e.

scholarly journals Spectral radius formulae

1979 ◽  
Vol 22 (3) ◽  
pp. 271-275 ◽  
Author(s):  
G. J. Murphy ◽  
T. T. West
Keyword(s):  
Banach Algebra ◽  
Spectral Radius ◽  
Quotient Algebra ◽  
Complex Banach Algebra ◽  
Image Position

If A is a complex Banach algebra (not necessarily unital) and x∈A, σ(x) will denote the spectrum and spectral radius of x in A. If I is a closed two-sided ideal in A let x + I denote the coset in the quotient algebra A/I containing x. Then

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
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