On the local spectra of seminormal operators

Clancey, Kevin F.

doi:10.1090/S0002-9939-1978-0509237-2

On the local spectra of seminormal operators
HTML articles powered by AMS MathViewer

by Kevin F. Clancey PDF

Proc. Amer. Math. Soc. 72 (1978), 473-479 Request permission

Abstract:

Two theorems on the local spectra of seminormal operators are deduced. In the first theorem it is shown that when T is hyponormal any solution of the equation $(T - \lambda )x(\lambda ) = x$ on an open set in the plane is necessarily analytic. The second theorem establishes the existence of vectors with small local spectra for a cohyponormal operator with a finite rank self-commutator.

References

Richard W. Carey and Joel D. Pincus, Mosaics, principal functions, and mean motion in von Neumann algebras, Acta Math. 138 (1977), no. 3-4, 153–218. MR 435901, DOI 10.1007/BF02392315
B. E. Johnson, Continuity of linear operators commuting with continuous linear operators, Trans. Amer. Math. Soc. 128 (1967), 88–102. MR 213894, DOI 10.1090/S0002-9947-1967-0213894-5
M. G. Kreĭn, On perturbation determinants and a trace formula for unitary and self-adjoint operators, Dokl. Akad. Nauk SSSR 144 (1962), 268–271 (Russian). MR 0139006
C. R. Putnam, Ranges of normal and subnormal operators, Michigan Math. J. 18 (1971), 33–36. MR 276810
C. R. Putnam, Hyponormal contractions and strong power convergence, Pacific J. Math. 57 (1975), no. 2, 531–538. MR 380493
M. Radjabalipour, Ranges of hyponormal operators, Illinois J. Math. 21 (1977), no. 1, 70–75. MR 448140
Joseph G. Stampfli, A local spectral theory for operators. V. Spectral subspaces for hyponormal operators, Trans. Amer. Math. Soc. 217 (1976), 285–296. MR 420325, DOI 10.1090/S0002-9947-1976-0420325-4
Joseph G. Stampfli and Bhushan L. Wadhwa, On dominant operators, Monatsh. Math. 84 (1977), no. 2, 143–153. MR 458225, DOI 10.1007/BF01579599