# DRAZIN INVERSES OF OPERATORS WITH RATIONAL RESOLVENT

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This paper deals with some approximation techniques for operators from the algebra (Qg(X))0 extending the known case of operators on Banach spaces. Those techniques are widely used in computational problems especially in medical fields.

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Let $p$ be an $m$-homogeneous polynomial on a complex Banach space, and let $(x_n)_n$ be a bounded sequence such that when evaluated in polynomials of degree less than $m$, it converges to zero, but $p(x_n)=1$. It is proved here that there exists...

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Two results are proved about the Banach space X = î”¢(K), where K is compact and Hausdorff. The first concerns smooth approximation: let m be a positive integer or âˆž; we show that if there exists on X a non-zero function of class î”¢m with bounded support, then all continuous...

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We prove strong convergence of the viscosity approximation process for nonexpansive nonself multimaps. Furthermore, an explicit iteration process which converges strongly to a fixed point of multimap T is constructed. It is worth mentioning that, unlike other authors, we do not impose the...

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If L ? 0 is a continuous symmetric n-linear form on a Banach space and is the associated continuous n-homogeneous polynomial, the ratio always lies between 1 and nn/n!. At one extreme, if L is defined on Hilbert space, then . If L attains norm on Hilbert space, then also attains norm; in...

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We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm...

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This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.