ON STAR MOMENT SEQUENCE OF OPERATORS

• Journal title : Honam Mathematical Journal
• Volume 29, Issue 4,  2007, pp.569-576
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2007.29.4.569
Title & Authors
ON STAR MOMENT SEQUENCE OF OPERATORS
Park, Sun-Hyun;

Abstract
Let $\small{\cal{H}}$ be a separable, infinite dimensional, complex Hilbert space. We call "an operator $\small{\cal{T}}$ acting on $\small{\cal{H}}$ has a star moment sequence supported on a set K" when there exist nonzero vectors u and v in $\small{\cal{H}}$ and a positive Borel measure $\small{{\mu}}$ such that <$\small{T^{*j}T^ku}$, v> = $\small{{^\int\limits_{K}}\;{{\bar{z}}^j}\;{{\bar{z}}^k}\;d\mu}$ for all j, $\small{k\;\geq\;0}$. We obtain a characterization to find a representing star moment measure and discuss some related properties.
Keywords
moment sequence;invariant subspace;essentially normal operator;subnormal operator;
Language
English
Cited by
References
1.
C. Apostol, C. Foias and D. Voiculescu, Some results on non-quasitriangular operators, IV, Revue Roum. de Math. Pure. Appl. 18 (1973), 487-514.

2.
A. Atzmon and G. Godefroy, An application of the smooth variational principle to the existence of nontrivial invariant subspaces, Compo. R. I'Acad. Sci. Paris, Serie I, Math. 332(2001), 151-156.

3.
L. Brown, R. G. Douglas and P. Fillmore, Extensions of $C^{*}$-algebras and K-homology, Ann. Math. 105 (1977), 265-324.

4.
C. Foias, I. Jung, E. Ko and C. Pearcy, Operators that admit a moment sequence, Israel J. Math. 145 (2005), 83-91.

5.
B. Chevreau, I. Jung, E. Ko and C. Pearcy, Operators that admit a moment sequence, II, Proc. the Amer. Math. Soc., 135 (2007), 1763-1767.

6.
D. Voiculescu, A note on quasitriangularity and trace-class self-commutators, Acta Sci. Math. (Sz.) 42 (1980), 1303-1320.