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Spectral Approximation and Index for Convolution Type Operators on Cones on L(p)(R(2))

Author:
Mascarenhas, H.  Silbermann, B.  


Journal:
INTEGRAL EQUATIONS AND OPERATOR THEORY


Issue Date:
2009


Abstract(summary):

We consider an algebra of operator sequences containing, among others, the approximation sequences to convolution type operators on cones acting on L(p)(R(2)), with 1 < p < infinity. To each operator sequence (A(n)) we associate a family of operators W(x)(A(n)) is an element of L(L(p)(R(2))) parametrized by x in some index set. When all W(x)(A(n)) are Fredholm, the so-called approximation numbers of An have the alpha-splitting property with a being the sum of the kernel dimensions of W(x)(A(n)). Moreover, the sum of the indices of W(x)(A(n)) is zero. We also show that the index of some composed convolution-like operators is zero. Results on the convergence of the epsilon-pseudospectrum, norms of inverses and condition numbers are also obtained.


Page:
415---448


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