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ArticleOriginal scientific text
Title
Compact AC-operators
Authors 1, 1
Affiliations
- School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia
Abstract
We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.
Keywords
AC-operators
Bibliography
- [BDG] E. Berkson, I. Doust and T. A. Gillespie, Properties of AC-operators, preprint.
- [BG] E. Berkson and T. A. Gillespie, Absolutely continuous functions of two variables and well-bounded operators, J. London Math. Soc (2) 30 (1984), 305-321.
- [CD] Q. Cheng and I. Doust, Well-bounded operators on nonreflexive Banach spaces, Proc. Amer. Math. Soc., to appear.
- [DdL] I. Doust and R. deLaubenfels, Functional calculus, integral representations, and Banach space geometry, Quaestiones Math. 17 (1994), 161-171.
- [DQ] I. Doust and B. Qiu, The spectral theorem for well-bounded operators, J. Austral. Math. Soc. Ser. A 54 (1993), 334-351.
- [Dow] H. R. Dowson, Spectral Theory of Linear Operators, London Math. Soc. Monographs 12, Academic Press, London, 1978.
- [R] J. R. Ringrose, On well-bounded operators, J. Austral. Math. Soc. Ser. A 1 (1960), 334-343.
- [Sm] D. R. Smart, Conditionally convergent spectral expansions, ibid. 1 (1960), 319-333.