On semi-normal operators

On the Spectra of Semi-normal Operators

On the Structure of Semi-normal Operators

1. Preliminaries. Only bounded operators on a Hilbert space § of elements x will be considered. If A is self-ad joint with the spectral resolution (1) A=f\dE(k), and if ^a = £>aC4) denotes the set of elements x for which ||E(X)#|| is an absolutely continuous function of X, then § 0 is a subspace; cf. [2, p. 240], [3, p. 436] and [6, p. 104]. If £ = £«, then A is called absolutely continuous. Th...

Semi-groups of Operators

Remarks on Hyponormal Operators and Almost Normal Operators

In 1984 M. Putinar proved that hyponormal operators are subscalar operators of order two. The proof provided a concrete structure of such operators. We will use this structure to give a sufficient condition for hyponormal operators T with trace-class commutator to admit a direct summand S so that T ⊕ S is the sum of a normal operator and a HilbertSchmidt operator. We investigate what this suffi...

Semi-normal Schedulings: Improvement on Goemans' Algorithm

Theoretical study of the multiprocessor job scheduling problem has made significant progress recently, which, however, seems not yet to imply practical algorithms. This paper offers new observations and introduces new techniques for the multiprocessor job scheduling problem P3|fix|Cmax. The concept of semi-normal schedulings is introduced and a very simple linear time algorithm for constructing...