Over the past decade, a pair of synchronization instructions known as LL/SC has emerged as the most suitable set of instructions to be used in the design of lock-free algorithms. However, no existing multiprocessor system supports these instructions in hardware. Instead, most modern multiprocessors support instructions such as CAS or RLL/RSC (e.g. POWER4, MIPS, SPARC, IA-64). This paper presents two efficient algorithms that implement 64-bit LL/SC from 64-bit CAS or RLL/RSC. Our re~ults are summarized as follows.We present a practical algorithm for implementing a 64-bit LL/SC object from 64-bit CAS or RLL/RSC objects. Our result shows, for the first time, a practical way of simulating a 64-bit LL/SC memory word using 64-bit CAS memory words (or 64-bit RLL/RSC memory words), incurring only a small constant space overhead per process and a small constant factor slowdown.Although our first solution performs correctly in any practical system, its theoretical correctness depends on unbounded sequence numbers. We present a bounded algorithm that implements a 64-bit LL/SC object from 64-bit CAS or RLL/RSC objects, and has the same time and space complexities as the first algorithm.This and the previous algorithm improve on existing implementations of LL/SC objects by

Abstract. In this paper we consider the integral Volterra operator on the space L 2 ð0; 1Þ. We say that a complex number is an extended eigenvalue of V if there exists a nonzero operator X satisfying the equation XV ¼ VX. We show that the set of extended eigenvalues of V is precisely the interval ð0; 1Þ and the corresponding eigenvectors may be chosen to be integral operators as well.

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We introduce a new class of operator algebras on Hilbert space. To each bounded linear operator a spectral algebra is associated. These algebras are quite substantial, each containing the commutant of the associated operator, frequently as a proper subalgebra. We establish several sufficient conditions for a spectral algebra to have a nontrivial invariant subspace. When the associated operator is compact this leads to a generalization of Lomonosov's theorem. r 2004 Elsevier Inc. All rights reserved. MSC: primary 47A65; secondary 47B49; 47B38

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