|
|
|
Classification of multiple unilateral weighted shifts by A?0 |
Juexian LI( ) |
| School of Mathematics, Liaoning University, Shenyang 110036, China |
|
|
|
|
Abstract In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes An(1≤n≤?0). As a result, we perfect and generalize the previous conclusions given by H. Bercovici, C. Foias, and C. Pearcy. Moreover, we remark that Question 21 posed by Shields has been negatively answered.
|
| Keywords
Multiple unilateral weighted shifts
An')" href="#">classes An
|
|
Corresponding Author(s):
LI Juexian,Email:juexianli@sina.com
|
|
Issue Date: 01 June 2012
|
|
| 1 |
Bercovici H. A contribution to the structure theory of operators in the class A. J Funct Anal , 1988, 78: 197-207
doi: 10.1016/0022-1236(88)90118-8
|
| 2 |
Bercovici H. Factorization theorem and the structure of operators on Hilbert space. Ann Math , 1988, 128: 399-413
doi: 10.2307/1971446
|
| 3 |
Bercovici H, Foias C, Pearcy C. Dilation theory and systems of simultaneous equations in the predual of an operator algebra I. Michigan Math J , 1983, 30: 335-354
doi: 10.1307/mmj/1029002909
|
| 4 |
Bercovici H, Foias C, Pearcy C. Dual Algebras with Applications to Invariant Subspaces and Dilation Theory. CBMS Regional Conference Ser in Math, No 56. Providence: Amer Math Soc, 1985
|
| 5 |
Chevreau B. Sur les contractions à calcul fonctionnel isométrique. J Operator Theory , 1988, 20: 269-293
|
| 6 |
Halmos P R. A Hilbert Space Problem Book. 2nd ed. Berlin-New York: Springer- Verlag, 1982
doi: 10.1007/978-1-4684-9330-6
|
| 7 |
Herrero D A. The Fredholm structure of on n-multicyclic operators. Indiana Univ Math J , 1987, 36: 549-566
doi: 10.1512/iumj.1987.36.36030
|
| 8 |
Lü F, Liu L F. The characterizations of shift operators being universal dilations. Science in China, Ser A , 1992, 35: 1017-1025 (in Chinese)
|
| 9 |
Makai E, Zemánek J. The surjectivity radius, packing numbers and boundedness below of linear operators. Integral Equations Operator Theory , 1983, 6: 372-384
doi: 10.1007/BF01691904
|
| 10 |
Shields A L. Weighted shift operators and analytic function theory. In: Topics in Operator Theory, Math Surveys, Vol 13. Providence: Amer Math Soc, 1974, 49-128
|
| 11 |
Sz.-Nagy B, Foias C. Harmonic Analysis of Operators on Hilbert Space. Amsterdam: North-Holland, 1970
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
