The canonical form of a scalar operator on a Banach space
Authors: G. D. Faulkner and J. E. Huneycutt
Journal: Proc. Amer. Math. Soc. 71 (1978), 81-84
MSC: Primary 47B40; Secondary 46G10
MathSciNet review: 0487577
Abstract: Let be a scalar operator on a Banach space X. If there exists a vector such that the closed convex hull of the range of the vector measure has nonvoid interior, then A is similar to the operator on a quotient space of a suitably constructed space.
-  N. I. Akhiezer and I. M. Glazman, The theory of linear operators in Hilbert space, Ungar, New York, 1963.
-  Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, With the assistance of William G. Bade and Robert G. Bartle, Interscience Publishers John Wiley & Sons New York-London, 1963. MR 0188745
-  Igor Kluvánek and Greg Knowles, Vector measures and control systems, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1976. North-Holland Mathematics Studies, Vol. 20; Notas de Matemática, No. 58. [Notes on Mathematics, No. 58]. MR 0499068
- N. I. Akhiezer and I. M. Glazman, The theory of linear operators in Hilbert space, Ungar, New York, 1963.
- N. Dunford and J. T. Schwartz, Linear operators, Interscience, New York, 1963. MR 0188745 (32:6181)
- I. Kluvanek and G. Knowles, Vector measures and control systems, New York, 1976. MR 0499068 (58:17033)