Compact AC-operators

• Autorzy: Ian Doust , Byron L. Walden
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

AC-operators

Kategorie tematyczne

• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995-1996
• Tom: 117
• Numer: 3
• Strony: 275-287

Daty

wydano

1996

otrzymano

1995-06-08

poprawiono

1995-08-13

Twórcy

autor

Ian Doust

• School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia,

autor

Byron L. Walden

• School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia,

Bibliografia

• [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.