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1. CJM 2012 (vol 65 pp. 989)
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 |
2. CJM 2009 (vol 62 pp. 74)
Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces |
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 |
3. CJM 2000 (vol 52 pp. 1057)
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 |