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Search: All articles in the CJM digital archive with keyword spectrum

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1. CJM Online first

Kaniuth, Eberhard
The Bochner-Schoenberg-Eberlein property and spectral synthesis for certain Banach algebra products
Associated with two commutative Banach algebras $A$ and $B$ and a character $\theta$ of $B$ is a certain Banach algebra product $A\times_\theta B$, which is a splitting extension of $B$ by $A$. We investigate two topics for the algebra $A\times_\theta B$ in relation to the corresponding ones of $A$ and $B$. The first one is the Bochner-Schoenberg-Eberlein property and the algebra of Bochner-Schoenberg-Eberlein functions on the spectrum, whereas the second one concerns the wide range of spectral synthesis problems for $A\times_\theta B$.

Keywords:commutative Banach algebra, splitting extension, Gelfand spectrum, set of synthesis, weak spectral set, multiplier algebra, BSE-algebra, BSE-function
Categories:46J10, 46J25, 43A30, 43A45

2. CJM 2012 (vol 65 pp. 989)

Chu, C-H.; Velasco, M. V.
Automatic Continuity of Homomorphisms in Non-associative Banach Algebras
We introduce the concept of a rare element in a non-associative normed algebra and show that the existence of such element is the only obstruction to continuity of a surjective homomorphism from a non-associative Banach algebra to a unital normed algebra with simple completion. Unital associative algebras do not admit any rare element and hence automatic continuity holds.

Keywords:automatic continuity, non-associative algebra, spectrum, rare operator, rare element
Categories:46H40, 46H70

3. CJM 2009 (vol 62 pp. 74)

Ducrot, Arnaud; Liu, Zhihua; Magal, Pierre
Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces
We present the explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues for linear neutral functional differential equations (NFDE) in $L^{p}$ spaces by using integrated semigroup theory. The analysis is based on the main result established elsewhere by the authors and results by Magal and Ruan on non-densely defined Cauchy problem. We formulate the NFDE as a non-densely defined Cauchy problem and obtain some spectral properties from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues. Such explicit formulas are important in studying bifurcations in some semi-linear problems.

Keywords:neutral functional differential equations, semi-linear problem, integrated semigroup, spectrum, projectors
Categories:34K05, 35K57, 47A56, 47H20

4. CJM 2000 (vol 52 pp. 1057)

Urakawa, Hajime
The Spectrum of an Infinite Graph
In this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential) spectrum for several examples of infinite graphs.

Keywords:infinite graph, discrete Laplacian, spectrum, essential spectrum
Categories:05C50, 58G25

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