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On an Algebra Generated by Abstract Singular Operators and a Shift Operator

✍ Scribed by N. L. Vasilevski

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
687 KB
Volume
162
Category
Article
ISSN
0025-584X

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✦ Synopsis

Let M(clR") be a smooth compact manifold. Recall (see, for instance, [3, 61) that a bounded linear operator S in L,(M) is called an abstract singular operator if the following conditions (axioms) hold:

  1. the operator S2 -I is compact (and the operators S f Z are noncompact); 2. the operator S* -S is compact;

πŸ“œ SIMILAR VOLUMES

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Let \(G\) be a locally compact group and \(\mathrm{VN}(G)\) be the von Neumann algebra generated by the left regular representation of \(G\). Let \(\operatorname{UCB}(\hat{G})\) denote the \(C^{*}\)-subalgebra generated by operators in \(\mathrm{VN}(G)\) with compact support. When \(G\) is abelian.

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## Abstract A system of ordinary differential operators of mixed order on an interval (0,Ο„~0~), __r__~o~0 > 0, is considered, where the coefficients may be singular at 0. A special case has been dealt with by Kako where the essential spectrum of an operator associated with a linearized magnetohydro