1980
DOI: 10.1090/s0002-9939-1980-0550494-3
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Equality of essential spectra of certain quasisimilar seminormal operators

Abstract: Abstract. Let A and B be quasisimilar seminormal operators on a separable, infinite dimensional complex Hilbert space. Several conditions which imply that A and B have equal essential spectra are presented. For example, if A and B are both biquasitriangular then A and B have equal essential spectra.Let DC denote a separable, infinite dimensional complex Hilbert space, and let £(DC) denote the algebra of all bounded linear operators on DC. (We shall use the term operator to mean an element of £(DC). Unless spec… Show more

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Cited by 4 publications
(3 citation statements)
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“…Note that the problem of looking for conditions under which the essential spectrum is equal to spectrum of a given operator has also been considered by a number of authors. In particular, Williams (1980) managed to show that there are several cases under which quasisimilar operators A and B have equal essential spectra also proved the following result on equality of spectrum and essential spectrum for a given operator.…”
Section: Remarkmentioning
confidence: 95%
“…Note that the problem of looking for conditions under which the essential spectrum is equal to spectrum of a given operator has also been considered by a number of authors. In particular, Williams (1980) managed to show that there are several cases under which quasisimilar operators A and B have equal essential spectra also proved the following result on equality of spectrum and essential spectrum for a given operator.…”
Section: Remarkmentioning
confidence: 95%
“…It is interesting to contrast these positive results with the known negative ones: (1) there are quasisimilar c.n.n. quasinormal operators which are not similar to each other [19,Example 2]; (2) there are c.n.n. subnormal operators similar to a simple unilateral shift without being unitarily equivalent to it [9,Solution 199].…”
Section: Proofmentioning
confidence: 99%
“…Clary [1,Theorem 2] proved that quasisimilar hyponormal operators have equal spectra and asked whether quasisimilar hyponormal operators also have essential spectra. Later Williams (see [11,Theorem 1], [12,Theorem 3]) showed that two quasisimilar quasinormal operators and under certain conditions two quasisimilar hyponormal operators have equal essential spectra. Gupta [4,Theorem 4] showed that biquasitriangular and quasisimilar k-quasihyponormal operators have equal essential spectra.…”
Section: Introductionmentioning
confidence: 99%